Chapter 8, Problem 44RE

(A)

To determine

To calculate:The value of $P\left(R\left|U_1\right.\right)$, if the urn is selected randomly by flipping a fair coin and then the ball is drawn from the urn. There are two urns, urn $U_1$ contains $2$ white balls and $3$ red balls, and urn $U_2$ contains $2$ white balls and $1$ red ball.

(B)

To determine

To calculate:The value of $P\left(R\left|U_2\right.\right)$, if the urn is selected randomly by flipping a fair coin and then the ball is drawn from the urn. There are two urns, urn $U_1$ contains $2$ white balls and $3$ red balls, and urn $U_2$ contains $2$ white balls and $1$ red ball.

(C)

To determine

To calculate:The value of $P\left(U_2\left|W\right.\right)$, if the urn is selected randomly by flipping a fair coin, and then the ball is drawn from the urn. There are two urns, urn $U_1$ contains $2$ white balls and $3$ red balls, and urn $U_2$ contains $2$ white balls and $1$ red ball.

(D)

To determine

To calculate:The value of $P\left(U_1\left|R\right.\right)$, if the urn is selected randomly by flipping a fair coin, and then the ball is drawn from the urn. There are two urns, urn $U_1$ contains $2$ white balls and $3$ red balls, and urn $U_2$ contains $2$ white balls and $1$ red ball.