# Exam P Practice Problem 98 – flipping coins

Problem 98-A

Coin 1 is an unbiased coin, i.e. when flipping the coin, the probability of getting a head is 0.5. Coin 2 is a biased coin such that when flipping the coin, the probability of getting a head is 0.6. One of the coins is chosen at random. Then the chosen coin is tossed repeatedly until a head is obtained.

Suppose that the first head is observed in the fifth toss. Determine the probability that the chosen coin is Coin 2. $\text{ }$ $\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ 0.2856$ $\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ 0.3060$ $\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ 0.3295$ $\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ 0.3564$ $\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ 0.3690$ $\text{ }$ $\text{ }$ $\text{ }$

Problem 98-B

Box 1 contains 3 red balls and 1 white ball while Box 2 contains 2 red balls and 2 white balls. The two boxes are identical in appearance. One of the boxes is chosen at random. A ball is sampled from the chosen box with replacement until a white ball is obtained.

Determine the probability that the chosen box is Box 1 if the first white ball is observed on the 6th draw. $\text{ }$ $\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ 0.7530$ $\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ 0.7632$ $\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ 0.7825$ $\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ 0.7863$ $\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ 0.7915$ $\text{ }$ $\text{ }$ $\text{ }$ $\text{ }$ $\text{ }$ $\text{ }$ $\text{ }$ $\text{ }$

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