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  4. 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

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Q. 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

JEE MainJEE Main 2023Probability - Part 2

Solution:

$ \frac{{ }^5 C _2+{ }^6 C _2}{{ }^2 C _2+{ }^3 C _2+{ }^4 C _2+{ }^5 C _2+{ }^8 C _2}=\frac{10+15}{1+3+6+10+15} $
$ =\frac{25}{35}=\frac{5}{7}$