# Probability of $2$ bags containing white and black balls.

A bag contains $4$ white balls and $2$ black balls , another contains $3$ white balls and $5$ black balls . If one ball is drawn from each bag, determine the probability that both are white .

$a.)\ \dfrac13 \\ b.)\ \dfrac23 \\ \color{green}{ c.)\ \dfrac14 } \\ d.)\ \dfrac34$

I did $\dfrac12 \times \dfrac46 + \dfrac12 \times \dfrac38=\dfrac{25}{48}$

But the answer is given as option $c.)$

I look for a short and simple way .

I have studied maths upto $12$th grade.

• You are selecting one ball from each bag, so the probability that you select a ball from the first bag is $1$, as is the probability that you select a bag from the second bag. Moreover, when you perform two independent tasks, the probabilities multiply. You add the probabilities when two tasks are mutually exclusive. – N. F. Taussig Oct 19 '15 at 19:24

Probability that the ball from first bag is white=$4/6$
Probability that the ball from second bag is white=$3/8$
So the answer is $4/6\times3/8=1/4.$