Question

A bag contains 2 white balls, 3 red balls . Another bag contains 4 white balls , 2 red balls . A bag and a ball are chosen at random . Find the probability of getting a white ball

Answer 1

Here, use the formula, $Probability=\frac{Numberoffavourableoutcomes}{Totalnumberofoutcomes}$.
Now, for bag I
Number of white balls = 2
Number of red balls = 3
Total number of balls = 2 + 3
= 5
$Probability\left(ofgettingawhiteball\right)=\frac{2}{5}$

Similarly, for bag II
Number of white balls = 4
Number of red balls = 2
Total number of balls = 4 +2
= 6
$$\begin{gathered} Probability\left(ofgettingawhiteball\right)=\frac{4}{6} \\ Probability\left(ofgettingawhiteball\right)=\frac{2}{3} \end{gathered}$$

Now, if a bag and ball are chosen at random;
$$\begin{gathered} Probability(ofgettingwhiteball)=\frac{2}{5}\times \frac{2}{3} \\ Probability(ofgettingwhiteball)=\frac{4}{15} \end{gathered}$$

Thus, the probability of getting a white ball if a bag is chosen at random is 4/15