Reference no: EM132880255

1. There are 2,598,960 possible S-card hands that can be dealt with from an ordinary 52-card deck. In a 5-card hand of poker, a flush is a hand where all 5 cards are of the same suit. Assuming a well-shuffled deck of cards and a random deal, what is the probability of being dealt a flush? Show the formula you would use with numbers substituted in, but you do not need to solve all the way out.

2. When two six-sided dice are rolled, the probability of getting a one on both is 1/36. This means which of the following listed below. Choose the best answer and then briefly explain.

A. Of every 36 rolls, exactly 1 will have both die be one.
B. In the long run, the average number of ones is 1/36.
C. In the long run the outcome that both die are one will occur on 1/36 of all rolls.

3. Dr. Stats plans to toss a fair coin 10,000 times in the hope that it will lead him to a deeper understanding of the laws of probability. Which of the following statements is true? Explain your choice, meaning why is your choice true and the other choices false.

A. It is unlikely that Dr. Stats will get more than 5,000 heads.
B. Whenever Dr. Stats gets a string of 15 tails in a row, it becomes more likely that the next toss will be a head.
C. The fraction of tosses resulting in heads should be close to 1/2.
D. The chance that the 100th toss will be a head depends somewhat on the results of the first 99 tosses.
E. All of the above statements are true.

4. A card is drawn from a well-shuffled deck of 52 playing cards. What is the probability that it is a queen or a heart?

5.A fair die is tossed, and the up face is noted. If the number is even, the die is tossed again; if the number is odd, a fair coin is tossed. Define the events:

A: {A head appears on the coin} and B: {The die is tossed only one time}

a) List the sample points in the sample space.
b) Give the probability for each of the sample points.
c) Find P(A) and P(B).
d) Identify the sample points in A^??, B^??, A∩B, and A∪B
e) Find P(A^??), P(B^??), P(A∩B), and P(A∪B)
f) Are A and B mutually exclusive events? Independent events? Why or why not?

6. A card is drawn from a well-shuffled deck of 52 playing cards. What is the probability that it is a queen or a heart? Tom either takes public transportation or bikes to work depending on how he feels in the morning. Over the past year, Tom took public transportation 35% of the time. On occasion, Tom is late to work, and the probability of being late depends on the mode of transportation. When traveling by public transportation, Tom is late 25% of the time. If he bikes, Tom is late 15% of the time.

Let L = Tom is late
Let B = Tom bikes to work

a) What information are you given in the problem? Write down the information using the two events that are defined.
b) What is the overall probability that Tom is late to work?
c) If Tom is late to work on a given day, what is the probability that he biked to work?