The probabilities of A, B, C solving a problem independently are respectively 4 1 , 5 1 , 6 1 . If 21 such problems are given to A , B , C then the probability that atleast 11 problems can be so

Question

The probabilities of A, B, C solving a problem independently are respectively 4 1 ​ , 5 1 ​ , 6 1 ​ . If 21 such problems are given to A , B , C then the probability that atleast 11 problems can be solved by them is

TestHub · Accepted Answer

No. of trials n = 21 Success is solving the problem ​ ∴ p = P ( A ∪ B ∪ C ) = 1 − P ( A ˉ ) P ( B ˉ ) P ( C ˉ ) ​ = 1 − 4 3 ​ × 5 4 ​ × 6 5 ​ ​ = 2 1 ​ ​ q = 2 1 ​ ​ Find P ( X ≥ 11 )

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