A bag contains 6 balls. Two balls are drawn from it at random and both are found to be black. The probability that the bag contains at least 5 black balls is :
Solution
Let $E_{i} \rightarrow$ Bag have at least $i$ black balls
<br/><br/>$E \rightarrow 2$ balls are drawn & both black
<br/><br/>$$
\begin{aligned}
& \therefore P\left(\frac{E_{5} \text { or } E_{6}}{E}\right)=\frac{P\left(\frac{E}{E_{5}}\right)+P\left(\frac{E}{E_{6}}\right)}{\sum\limits_{i=1}^{6} P\left(\frac{E}{E_{i}}\right)} \\\\
& =\frac{\frac{{ }^{5} C_{2}}{{ }^{6} C_{2}}+\frac{{ }^{6} C_{2}}{{ }^{6} C_{2}}}{0+\frac{{ }^{2} C_{2}}{{ }^{6} C_{2}}+\frac{{ }^{3} C_{2}}{{ }^{6} C_{2}}+\frac{{ }^{4} C_{2}}{{ }^{6} C_{2}}+\frac{{ }^{5} C_{2}}{{ }^{6} C_{2}}+\frac{{ }^{6} C_{2}}{{ }^{6} C_{2}}} \\\\
& =\frac{10+15}{1+3+6+10+15}=\frac{25}{35}=\frac{5}{7}
\end{aligned}
$$
About this question
Subject: Mathematics · Chapter: Probability · Topic: Classical and Axiomatic Probability
This question is part of PrepWiser's free JEE Main question bank. 143 more solved questions on Probability are available — start with the harder ones if your accuracy is >70%.