Question

Die $A$ has 4 red and 2 white faces, whereas die $B$ has 2 red and 4 white faces. A fair coin is flipped once. If it lands on heads, the game continues with dic $A ;$ if it lands on tails, then dic $B$ is to be used. (a) Show that the probability of red at any throw is $\frac{1}{2}.$ (b) If the first two throws result in red, what is the probability of red at the third throw? (c) If red turns up at the first two throws, what is the probability that it is die $A$ that is being used?

          Die $A$ has 4 red and 2 white faces, whereas die $B$ has 2 red and 4 white faces. A fair coin is flipped once. If it lands on heads, the game continues with dic $A ;$ if it lands on tails, then dic $B$ is to be used.
(a) Show that the probability of red at any throw is $\frac{1}{2}.$
(b) If the first two throws result in red, what is the probability of red at the third throw?
(c) If red turns up at the first two throws, what is the probability that it is die $A$ that is being used?

Added by Esther I.

Probability with Applications in Engineering, Science, and Technology

Matthew A. Carlton • Jay L. Devore 2nd Edition

Instant Answer

Solved by Expert Croup Chais

12/10/2021

Step 1

The probability of rolling red on die A is $\frac{4}{6} = \frac{2}{3}$. So the probability of both these events happening is $\frac{1}{2} \times \frac{2}{3} = \frac{1}{3}$. Similarly, the probability of getting tails on the coin flip (and thus using die B) is Show more…

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Die $A$ has 4 red and 2 white faces, whereas die $B$ has 2 red and 4 white faces. A fair coin is flipped once. If it lands on heads, the game continues with dic $A ;$ if it lands on tails, then dic $B$ is to be used. (a) Show that the probability of red at any throw is $\frac{1}{2}.$ (b) If the first two throws result in red, what is the probability of red at the third throw? (c) If red turns up at the first two throws, what is the probability that it is die $A$ that is being used?