Let $U_1$ and $U_2$ be two urns such that $U_1$ contains $3$ white and $2$ red balls,and $U_2$ contains only $1$ white ball. $A$ fair coin is tossed. If it shows head,$1$ ball is drawn at random from $U_1$ and transferred to $U_2$. If it shows tail,$2$ balls are drawn at random from $U_1$ and transferred to $U_2$. Now,$1$ ball is drawn at random from $U_2$. Given that the ball drawn from $U_2$ is white,what is the probability that the coin showed head?
- A$13/20$
- B$23/30$
- C$19/30$
- D$11/30$
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Similar Questions
Coloured balls are distributed in four boxes as shown in the following table:
Box Black White Red Blue $I$ $3$ $4$ $5$ $6$ $II$ $2$ $2$ $2$ $2$ $III$ $1$ $2$ $3$ $1$ $IV$ $4$ $3$ $1$ $5$
$A$ box is selected at random and then a ball is randomly drawn from the selected box. If the colour of the ball is black,what is the probability that the ball drawn is from box $III$?
| Box | Black | White | Red | Blue |
|---|---|---|---|---|
| $I$ | $3$ | $4$ | $5$ | $6$ |
| $II$ | $2$ | $2$ | $2$ | $2$ |
| $III$ | $1$ | $2$ | $3$ | $1$ |
| $IV$ | $4$ | $3$ | $1$ | $5$ |
$A$ box is selected at random and then a ball is randomly drawn from the selected box. If the colour of the ball is black,what is the probability that the ball drawn is from box $III$?
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