Question

A bag contains $5$ red and $3$ blue balls. If $3$ balls are drawn at random without replacement the probability of getting exactly one red ball is

• A. $\frac{135}{392}$
• B. $\frac{45}{196}$
• C. $\frac{15}{56}$
• D. $\frac{15}{29}$

Answer 1

The correct option is C $\frac{15}{56}$

Given Number of Red balls = $5$
Number of Blue balls = $3$
Total number of balls =$8$
∵Probability of an event $A$ 𝑖𝑠 :
$P\left(A\right)=\frac{\text{No.of favourable outcomes w.r.t.A}}{\text{Total outcomes of the experiment}}$
∴Probability of getting exactly one red ball is
$=P\left(R\right)\cdot P\left(\frac{B}{R}\right)\cdot P\left(\frac{B}{(R,B)}\right)$ $+P\left(B\right)\cdot P\left(\frac{R}{B}\right)\cdot P\left(\frac{B}{(B,R)}\right)$ $+P\left(B\right)\cdot P\left(\frac{B}{B}\right)\cdot P\left(\frac{R}{B,B}\right)$
$=\frac{5}{8}\cdot \frac{3}{7}\cdot \frac{2}{6}+\frac{3}{8}\cdot \frac{2}{7}\cdot \frac{5}{6}+\frac{3}{8}\cdot \frac{2}{7}\cdot \frac{5}{6}=\frac{15}{56}$
Hence option (𝐶) is correct.