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Problem: A bag contains 5 blue and 4 black balls. Three balls are drawn at random, what is the probability that 2 are blue and 1 is black? [ Calculator, Method and examples ]

Solution:
Your problem `->` A bag contains 5 blue and 4 black balls. Three balls are drawn at random, what is the probability that 2 are blue and 1 is black?


Total number of balls`=5+4=9`

Let `S` be the sample space.

Then, `n(S) = ` Total number of ways of drawing `3` balls out of `9`

`:.n(S) = {::}^9C_3=(9 * 8 * 7)/(3 * 2 * 1)=84`

Let `E=` Event of drawing 2 blue balls out of 5 and 1 black balls out of 4.

`n(E) = {::}^5 C_2 xx {::}^4 C_1`

`=(5 * 4)/(2 * 1) xx 4`

`=10 xx 4`

`=40`

`:.P(E)=(n(E))/(n(S))=40/84=10/21`








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