The probability that A will solve a problem is and B will solve it is . If both try the problem independently, find the probability that the problem will be solved. - Wired Faculty

Probability

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The probability that A will solve a problem is $2 over 5$ and B will solve it is $5 over 6$ . If both try the problem independently, find the probability that the problem will be solved.

Solution

The probabilities of A and B solving the problem are $2 over 5 space and space 5 over 6$ respectively.
$therefore$ the probabilities of A and B not solving the problems are $1 minus 2 over 5 comma space 1 space minus 5 over 6$ i.e., $3 over 5 comma space space 1 over 6$ respectively.
$therefore$ probabilities that problem is not solved by A and B $equals space 3 over 5 cross times 1 over 6 space equals 1 over 10$
$therefore$ probability that the problem will be solved = $1 minus 1 over 10 space equals space 9 over 10$

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Probability

The probability that A will solve a problem is $2 over 5$ and B will solve it is $5 over 6$ . If both try the problem independently, find the probability that the problem will be solved.

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