# A bag X contains 3 white balls and 2 black balls and another bag Y contains 2 white and 4 black balls [closed]

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?

## closed as off-topic by Aqua, NCh, Shailesh, Xander Henderson, qwrOct 16 '17 at 1:46

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Aqua, NCh, Shailesh, Xander Henderson, qwr
If this question can be reworded to fit the rules in the help center, please edit the question.

## 1 Answer

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 $P(W \mid Y)$ )

• 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. – N. F. Taussig Oct 15 '17 at 10:58
• Thank you N. F. Taussig, for your suggestions. – Suman Sahu Oct 15 '17 at 14:51