A bag X contains 3 white balls and 2 black balls and another bag Y contains 2 white and 4 black balls. A bag and a ball out of it are picked at random, the probability of ball being white is?


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Find the probability of choosing bag $X$ and the same for $Y$. Next, find the probability of getting a white ball from bag $X$ and that from bag $Y$. To find the final answer, multiply $P(X)$ with $P(W \mid X)$ and $P(Y)$ with $P(W \mid Y)$ and then add the products. You will find the answer to be $7/15$. Here, you can refer the topic of conditional probability. For finding $P(W)$, you have to add the probabilities of obtaining a white ball from bag $X$ and that from bag $Y$ ie $P(W)=P(X)P(W\mid X) + P(Y)P(W \mid Y)$

And in general, $P(A \mid B)$ refers to - the event of interest is $A$ and the event $B$ is known or assumed to have occurred. As in this case, the event of interest is choosing a white ball and the event known to us is choosing a bag $X$ (or $Y$ in case of $P(W \mid Y)$ )

  • $\begingroup$ Welcome to MathSE. Please read this tutorial on how to typeset mathematics on this site. In your answer, I suggest that you write down the formula you are using for $P(W)$ and that you explain what $P(W \mid X)$ and $P(W \mid Y)$ mean. $\endgroup$ – N. F. Taussig Oct 15 '17 at 10:58
  • $\begingroup$ Thank you N. F. Taussig, for your suggestions. $\endgroup$ – Suman Sahu Oct 15 '17 at 14:51

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