A bag contains 10 balls of two colours, the number of balls of each colour being same. 5 balls are drawn at random one by one. The ball in hand is returned to the bag before each new drawn, then probability that at least 2 balls of each colour are drawn is

Engineering

Mathematics

Conditional Probability

Question

$\frac{5}{16}$

$\frac{5}{8}$

None of these

$\frac{1}{2}$

LiveFree JEE Main Previous Year Online Papers Live Free JEE Advance Previous Year Online Papers

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

$P (s) = P = \frac{1}{2}, P (F) = \frac{1}{2}$ in one draw

$^{5} C_{2} {(\frac{1}{2})}^{2} {(\frac{1}{2})}^{3} +^{5} C_{3} {(\frac{1}{2})}^{5}$

$\Rightarrow {(\frac{1}{2})}^{5} (^{5} C_{2} +^{5} C_{3}) = \frac{5}{8}$