Reference no: EM133052016

Problem Set

Problem 1. A bucket contains identical 120 blue tickets and 200 red tickets. Suppose you are asked to draw one ticket from this bucket with eyes covered.

a. Give an example of a simple event and an example of a joint event.
b. What is the complement of having a red ticket?
c. What is the probability of drawing a blue ticket? Is this probability a priori classical probability, empirical classical probability, or subjective probability?

Problem 2. If P(A) = 0.7, P(B) = 0.1 and P(A∪B) = 0.8, then events A and B are

a. statistically independent b. mutually exclusive
c. complements d. collectively exhaustive

Problem 3. A sample of 500 people was asked whether they enjoyed shopping for children's toys. They were also asked whether they were under 40 years of age or 40 or more years of age. 240 people under 40 were chosen. Of these 136 said they enjoyed shopping for children's toys. 260 people 40 or more years of age were chosen. Of these, 224 said they enjoyed shopping for children's toys.

a. Construct a contingency table to show the probabilities.
b. What is the probability that someone enjoys shopping for children's toys?
c. What is the probability that someone is >=40 and enjoys shopping for children's toys?
d. What is the probability that someone is >=40 or enjoys shopping for children's toys?
e. What is the probability that someone is <40 or >= 40?
f. Are the probabilities in the question priori classical probabilities, empirical classical probabilities, or subjective probabilities?
g. What is the probability that someone enjoys shopping toys given that this person is under 40? Are the two event, enjoying shopping toys and being under 40 statistical independent?

Problem 4. A standard deck of 52 playing cards (4 suits - hearts, diamonds, clubs and spades, each suit with 13 cards: ace,2,3,4,5,6,7,8,9,10, jack, queen, king)) is being used to play a game. The deck is thoroughly mixed and you will receive the first 2 cards from the deck without replacement.

a. What is the probability that both cards are queens?
b. What is the probability that the first card is a 10 and the second a 5 or a 6?
c. If you were sampling with replacement, what would be the answer to part a.?
d. In the game of blackjack, the picture cards (jack, queen and king) count as 10 points and the ace counts as either 1 or 11. All other cards are counted as their face value. Blackjack is achieved if 2 cards total 21 points. What is the probability of getting blackjack (sampling without replacement)?

Problem 5. Machinists A and B produce the same fittings. A is slower and produces 3% defectives in his 40% of the firm's output. B produces 8% defects in his 60% of the firm's total output. A defective item is discovered. What is the probability it was produced by A?

Problem 6. The probability that a person has a certain disease is 0.03. Medical tests can be used to tell if the person has the disease. If the disease is actually present, the probability that the medical test will give a positive result is 0.9. If the disease is not present, the probability of a positive test is 0.01. Suppose that the medical test has given a positive result. What is the probability that the disease is actually present?

Problem 7. AMG is considering whether it should submit a tender for a new shopping centre. In the past, its main competitor, BFG has submitted a tender 70% of the time. If BFG doesn't submit a tender, the probability that AMG gets the job is 0.5. If BFG does submit a tender the probability that AMG gets the job is 0.25.
a. If AMG gets the job, what is the probability that BFG did not submit a tender?
b. What is the probability that AMG will get the job?