Reference no: EM132311683
Question 1. Life Insurance: A life insurance company wants to estimate the probability that a 40-year-old male will live through the next year. In a sample of 7000 such men from prior years, 6996 lived through the year. Use the relative frequency approximation to estimate the probability that a randomly selected 40-year-old male will live through the next year. Round your answer to 4 decimal places.
P(he lives through the year) =
Question 2. Lottery: You enter a lottery by purchasing one of the 500 tickets. There is 1 grand prize winner, 4 second prize winners, and 9 small prize winners. These are selected at random from a bin containing all the tickets.
(a) What is the probability that you will win the grand prize? Express your answer as an exact decimal (not a percent and do not round).
(b) What is the probability that you will win a prize of some type? Express your answer as an exact decimal (not a percent and do not round).
Question 3. Same Birthday: Suppose two people are randomly selected from a class of 40 students. What is the probability that they have the same birthday? Round your answer to 3 significant digits*.
*Significant Digits: Here are some probabilities expressed to 3 significant digits.
You start counting digits from left to right starting with the first non-zero digit.
0.123 0.0123 0.00123 0.102 0.350 0.300
Question 4. Cards: Suppose you draw one card from a single deck of cards.
(a) What is the probability that you draw an queen? Round your answer to 3 significant digits*.
(b) What is the probability that you draw a club? Round your answer to 3 significant digits*.
(c) What is the probability that you draw the queen of clubs? Round your answer to 3 significant digits*.
*Significant Digits: Here are some probabilities expressed to 3 significant digits.
You start counting digits from left to right starting with the first non-zero digit.
0.123 0.0123 0.00123 0.102 0.350 0.300
...............................................
Background playing card information: In a standard deck of playing cards there are 52 cards total. There are 4 suits:
hearts ♥ diamonds ♦ spades ♠ clubs ♣
Each suit has 13 values:
2 3 4 5 6 7 8 9 10 jack queen king ace
Question 5. Weather Forecast: The table below indicates the accuracy of a local weather report with respect to rain or no rain over the past year. This table gives the results of 365 consecutive days and compares whether it rained or not to whether or not rain was predicted.
|
Did it actually rain?
|
|
Yes No
|
|
Report Predicted Rain
|
108 14
|
|
Report Predicted No Rain
|
39 204
|
If one day is randomly selected from these 365 days, what is the probability of the following? (Round your answers to 3 significant digits*.)
(a) the prediction was correct
P(the prediction was correct) =
(b) it rained given that it was predicted to rain
P(it rained | rain was predicted) =
(c) it did not rain when it was predicted to not rain
P(no rain | no rain was predicted) =
(d) Based on these results, is this weather forecast better at predicting rain or better at predicting no rain?
The weather forecast is better at predicting rain. The weather forecast is better at predicting no rain.
...............................................
*Significant Digits: Here are some probabilities expressed to 3 significant digits. You start counting digits from left to right starting with the first non-zero digit.
0.123 0.0123 0.0120 0.00123 0.102 0.350 0.300
Pregnancy Test: A pregnancy testing device is used by 1000 different women from a population of women who think they might be pregnant. The results are depicted in the contingency table below. Here, a positive test result means pregnancy is detected.
|
Was she actually pregnant?
|
|
Yes No
|
|
Positive Test Result
|
479 12
|
|
Negative Test Result
|
5 504
|
(a) Using the relative frequency approximation of probabilities, what is the probability that the device is correct? Round your answer to 3 significant digits.*
P(result is correct) =
(b) Suppose you are a woman about to take the test. Prior to taking the test, what is the probability of a false-positive? Round your answer to 3 significant digits.*
P(false positive) =
(c) Suppose you are a woman who takes the test and it comes back positive. Now, what is the probability that the test result is wrong? Round your answer to 3 significant digits.*
P(not pregnant | positive test result) =
(d) What statement is true about the probability of getting a false positive?
a. The probability of a false positive is not affected by the result of the test.
b. The probability of a false positive increases after a positive test result is obtained.
c. The probability of a false positive decreases after a positive test result is obtained.
...............................................
*Significant Digits: Here are some probabilities expressed to 3 significant digits. You start counting digits from left to right starting with the first non-zero digit.
0.123 0.0123 0.0120 0.00123 0.102 0.350 0.300
Cards: Suppose you and a friend are playing cards and you are each dealt 4 cards. You have a 10, jack, queen, and king in your hand. You are about to be dealt one more card. What is the probability that you are dealt an ace given the following? Round your answers to 3 significant digits*.
(a) your friend has no aces in her hand
(b) your friend has exactly one ace in her hand
...............................................
*Significant Digits: Here are some probabilities expressed to 3 significant digits.
You start counting digits from left to right starting with the first non-zero digit.
0.123 0.0123 0.0120 0.00123 0.102 0.350 0.300
...............................................
Background playing card information: In a standard deck of playing cards there are 52 cards total.
There are 4 suits:
hearts ♥ diamonds ♦ spades ♠ clubs ♣
Each suit has 13 values:
2 3 4 5 6 7 8 9 10 jack queen king ace
Cards: Suppose you are playing Poker alone. You have four cards (3♥, 4♥, 5♥, and 6♥). You are going to select one more card from the remaining deck. What is the probability that you get the following? Round your answers to 3 significant digits*.
(a) a flush (all cards of the same suit)
(b) a straight (5 consecutive cards)
(c) a straight flush (5 consecutive cards of the same suit)
...............................................
*Significant Digits: Here are some probabilities expressed to 3 significant digits.
You start counting digits from left to right starting with the first non-zero digit.
0.123 0.0123 0.0120 0.00123 0.102 0.350 0.300
...............................................
Background playing card information: In a standard deck of playing cards there are 52 cards total.
There are 4 suits:
hearts ♥ diamonds ♦ spades ♠ clubs ♣
Each suit has 13 values:
2 3 4 5 6 7 8 9 10 jack queen king ace
Mutually Exclusive Events: Determine whether the events are mutually exclusive or not.
(a) You roll a single, 6-sided die:
Event 1: getting a 6
Event 2: getting a 5
mutually exclusive not mutually exclusive
(b) One person is randomly selected from a group:
Event 1: selecting a person with brown eyes
Event 2: selecting a person with red hair
mutually exclusive not mutually exclusive
(c) One person is randomly selected from a group:
Event 1: selecting a person with brown eyes
Event 2: selecting a person with blue eyes
mutually exclusive not mutually exclusive
(d) A guy orders a meal at a restaurant:
Event 1: he orders a meal with vegetables
Event 2: he orders a vegetarian meal
mutually exclusive not mutually exclusive
Dice: Suppose you roll two 6-sided dice - a red one and a white one. There are 36 different outcomes in this sample space (for each of the 6 options on the red die, there are 6 options for the white one). Find the requested probabilities. Round your answers to 4 decimal places.
(a) What is the probability that the total on the dice is 3?
(b) What is the probability tat the total on the dice is not 3?
Ski Passes: The following table gives some information about a group of 200 college students. The rows tell whether or not the student has a car. The columns describe at which mountain the students have a ski pass.
Note: No student has a pass at more than one mountain.
Bolton Stowe Smuggler's Sugarbush No Pass
Has a Car 18 18 10 24 25
Does not have a Car 24 5 4 18 54
If one student is randomly selected, what is the probability that the following will occur? Round your answers to 3 significant digits*.
(a) The student has a pass at Stowe or Sugarbush.
P(Stowe or Sugarbush) =
(b) The student has a car or a pass to Sugarbush.
P(has a car or a pass at Sugarbush) =
(c) The student has a car or a ski pass somewhere.
P(has a car or has a pass)
...............................................
*Significant Digits: Here are some probabilities expressed to 3 significant digits.
You start counting digits from left to right starting with the first non-zero digit.
0.123 0.0123 0.0120 0.00123 0.102 0.350 0.300
Blood Types: The following table is an approximate summary of the blood types for 100 typical people. For example, a person with type O+ blood actually has Group O and Type Rh+ blood.
Type Group
O A B AB
Type Rh+ 42 31 8 4
Type Rh- 6 7 1 1
If one person is randomly selected from this group, what is the probability of the following? Enter your answers to 2 decimal places.
(a) selecting a person who is Group O or type Rh+
P(Group O or Type Rh+) =
(b) selecting a person who is Group A or Group B
P(Group A or Group B) =
Extended Multiplication Rule: Use the extended multiplication rule to calculate the following probabilities. Round your answers to 3 significant digits*.
(a) If you flip a fair coin 3 times, what is the probability of getting 3 heads?
(b) If you randomly select 4 people, what is the probability that they were born on the same day of the week (Monday, Tuesday, ... Sunday)?
(c) Assume that your car starts 99% of the time. What is the probability that your car will start for the next 14 days in a row? Assume these events are independent.
...............................................
*Significant Digits: Here are some probabilities expressed to 3 significant digits. You start counting digits from left to right starting with the first non-zero digit.
0.123 0.0123 0.0120 0.00123 0.102 0.350 0.300
Determine if the two events are dependent or independent.
(a) You play the lottery on Tuesday and play it again on Wednesday.
Event 1: winning the lottery on Tuesday
Event 2: winning the lottery on Wednesday
dependent independent
(b) You walk into your kitchen.
Event 1: the microwave doesn't work
Event 2: the refrigerator doesn't work
dependent independent
(c) You walk into your kitchen.
Event 1: the microwave doesn't work
Event 2: your left shoe is untied
dependent independent
Independent Events: Determine if the two events are dependent or independent.
(a) You flip a fair coin 4 times.
Event 1: getting heads on the first three tosses
Event 2: getting heads on the fourth toss
dependent independent
(b) There are 4 people (numbered 1 to 4) and you have to choose who will do a certain unpleasant task. You take 4 straws and cut one of them really short but hold them in your hand so that the contestants can't tell which straw is the short one. The contestants sequentially choose a straw and keep it. The person with the short straw has to do the unpleasant task.
Event 1: Person #1 draws the short straw
Event 2: Person #2 draws the short straw
dependent independent
Independent Events: Determine if the two events are dependent or independent.
(a) Two cards are drawn from a standard deck without replacement.
Event 1: getting a jack on the first draw
Event 2: getting a jack on the second draw
dependent independent
(b) Two cards are drawn from a standard deck with replacement.
Event 1: getting a jack on the first draw
Event 2: getting a jack on the second draw
dependent independent
(c) You buy two different gallons of milk at the same store.
Event 1: the first gallon is spoiled
Event 2: the second gallon is spoiled
dependent independent
Spark Plugs: Assume that 2% of all spark plugs are defective. Find the requested probabilities and round your answers to 3 significant digits*.
(a) If you buy one spark plug, what is the probability that it is not defective?
(b) If you buy 4 spark plugs, what is the probability that all 4 are not defective?
(c) If you buy 4 spark plugs, what is the probability that at least one is defective?
...............................................
*Significant Digits: Here are some probabilities expressed to 3 significant digits. You start counting digits from left to right starting with the first non-zero digit.
0.123 0.0123 0.0120 0.00123 0.102 0.350 0.300
At Least One Girl: Suppose a couple plans to have 4 children and the probability of a boy is 0.50. Find the probability that the couple has at least one girl. Round your answer to 3 significant digits*.
...............................................
*Significant Digits: Here are some probabilities expressed to 3 significant digits.
You start counting digits from left to right starting with the first non-zero digit.
0.123 0.0123 0.00123 0.102 0.350 0.300
Lie Detector: Suppose a lie detector test can detect a lie 95% of the time. You get hooked up and tell 10 truths and 10 lies. What is the probability that at least one of your lies goes undetected? Round your answer to 3 significant digits*.
...............................................
*Significant Digits: Here are some probabilities expressed to 3 significant digits.
You start counting digits from left to right starting with the first non-zero digit.
0.123 0.0123 0.0120 0.00123 0.102 0.350 0.300
Alarm Clock - Redundancy: You have two alarm clocks. The first one is successful 95% of the time and the second one is successful 69% of the time (it turns out your second one was actually less reliable than the first).
(a) Suppose you only remember to set the good alarm clock (the first one). What is the probability that it will succeed on the morning of an important exam? Enter your answer in decimal form to 2 decimal places.
(b) Suppose you set both alarm clocks. What is the probability that at least one of them is successful on the morning of an important exam? Round your answer to 3 significant digits* .
...............................................
*Significant Digits: Here are some probabilities expressed to 3 significant digits. You start counting digits from left to right starting with the first non-zero digit.
0.123 0.0123 0.0120 0.00123 0.102 0.350 0.300