Question

A bag contains $10$ white and $15$ black balls. Two balls are drawn without replacement find the probability that first is white and second is black........

• A. $\frac{1}{4}$
• B. $\frac{2}{7}$
• C. $\frac{1}{8}$
• D. $\frac{1}{5}$

Answer 1

The correct option is A $\frac{1}{4}$

Let $A$: be the event that first ball is white

And $B$: be the event that second ball is black

$P\left(A\right)=\frac{\text{Number of white balls}}{\text{Total number of balls}}=\frac{10}{25}=\frac{2}{5}$

$P\left(B\right)=\frac{\text{Number of black balls}}{\text{Total number of balls left}}=\frac{15}{24}=\frac{5}{8}$

{24 because 1 ball was taken out and not replaced}

Hence the probability that first is white and second is black $=$ $\frac{2}{5}\times \frac{5}{8}=\frac{1}{4}$