Question

One bag contains $3$ white and $2$ black balls, another bag contains $5$ white and $3$ black balls. If a bag is chosen at random and a ball is drawn from it, what is the change that it is white?

• A. $\frac{3}{8}$
• B. $\frac{49}{80}$
• C. $\frac{8}{13}$
• D. $\frac{1}{2}$

Answer 1

The correct option is B $\frac{49}{80}$

As the bag is chosen randomly so Probability of choosing each bag $=\frac{1}{2}$

Now for getting white ball from bag $1$ , first we have to choose bag $1$ and then a white ball from it.

So,

$P\left(W_1\right)=$Probability of choosing bag$1\times$ Probability of getting white ball from bag $1$

$P\left(W_1\right)=\frac{1}{2}\times \frac{3}{5}$

$P\left(W_1\right)=\frac{3}{10}$

Similarly,

$P\left(W_2\right)=$Probability of choosing bag $2\times$ Probability of getting white ball from bag $2$

$P\left(W_2\right)=\frac{1}{2}\times \frac{5}{8}$

$P\left(W_2\right)=\frac{5}{16}$

So,

Total probability of getting white ball from any bag is$=P\left(W_1\right)+P\left(W_2\right)$

$\Rightarrow \frac{3}{10}+\frac{5}{16}$

$\Rightarrow \frac{49}{80}$

Hence, the answer is $\frac{49}{80}$.