Question

1.

a.) Suppose you draw 8 cards from a standard deck of 52 cards, one after the other, without replacement. Find the probability that the last card is a club given that the first 7 cards are clubs.

b.) An urn contains 6 green, 10 blue, and 17 red balls. You take 3 balls out of the urn, one after the other, without replacement. Find the probability that the third ball is green given that the first two balls were red.

c.) You roll two fair dice. Find the probability that the first die is a 6 given that the minimum of the two numbers is a 5.

d.) You toss a fair coin 7 times. Find the probability of no more than 6 heads given that at least one toss resulted in heads.

2.

a.) A bag contains 2 coins, one fair and the other with 2 heads. You pick 1 coin at random and flip it. What is the probability that you picked the fair coin given that the outcome of the toss was heads?

b.)You pick 2 cards from a standard deck of 52 cards. Find the probability that the first card was a heart given that the second card was a heart.

c.) A drawer contains six bags numbered 1-6, respectively. Bag i contains i blue balls and 5 green balls. You roll a fair die and then pick a ball out of the bag with the number shown on the die. What is the probability that the ball is blue?

Answer 1