29 Jun Suppose that you draw two cards from a well-shuffled
Question
29. Suppose that you draw two cards from a well-shuffled deck of 52 playing cards without replacement. What is the probability that the second card is an ace, given that the first card is not an ace?
31. Suppose that you draw two cards from a well-shuffled deck of 52 playing cards without replacement. What is the probability that the second card is a spade, given that the first card is not a spade?
33. An experiment consists of drawing two marbles from an urn and observing the color. There are 8 red marbles and 7 white marbles in the urn. Find the probability that both marbles are red, assuming:
A. The first marble is returned to the urn before the second marble is drawn.
B. The first marble is not returned to the urn before the second marble is drawn.
35. An experiment consists of selecting an urn and then removing a marble from the urn. There are 12 red marbles and 8 blue marbles in Urn 1, and there are 9 red marbles and 15 blue marbles in Urn 2. Assume the urns are equally likely to be selected. Find the probability that:
A. The marble is blue.
B. The marble is red.
C. Urn 2 is chosen and a blue marble is drawn.
D. A red marble is drawn from Urn 2.
E. A red marble is drawn, given that Urn 2 is selected.
F. A blue marble is drawn, given that Urn 1 is selected.
37. An experiment consists of selecting two marbles from an urn, in succession and without replacement. The urn contains 14 green marbles and 11 yellow marbles. Find the probability that:
A. The second marble is green.
B. The second marble is yellow.
C. Both marbles are yellow.
D. Both marbles are green.
E. The second marble is green, given that the first marble is green.
F. The second marble is yellow, given that the first marble is green.
A single card is drawn randomly from a standard deck. Use the definition of independent events to determine if events A and B are independent.
Recall: The definition of independent events states that events A and B are independent if and only if P(A) = P(A|B).
41. Event A: Drawing a heart
Event B: Drawing an Ace
43. Event A: Drawing a black card
Event B: Drawing a heart
45. Event A: Drawing a diamond
Event B: Drawing a red card
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