Question 28

The probabilities that A, B, and D can solve a problem independently are $$\dfrac{1}{3},\ \dfrac{1}{3}\ \&\ \dfrac{1}{4}$$ respectively. The probability that only two of them are able to solve the problem is:

Solution

There are three cases for exactly two solving it right :
Case I : A, B solving correct and D going wrong
Probability = (1/3)(1/3)(3/4) = 1/12

Case II : A, D solving correct and B going wrong
Probability = (1/3)(2/3)(1/4) = 1/18

Case III : B,D solving correct and A going wrong
Probability = (2/3)(1/3)(1/4) = 1/18

Therefore, total probability = 1/12 + 1/18 + 1/18 = 1/12 + 1/9 = 7/36

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