Please type your question here Two students are working inde

Please type your question here: Two students are working independently on a problem. Their respective probabilities of solving the problem are 1/3 and 3/4.

a. What is the probability that both of them will solve the problem?

b. What is the probability that at least one of them will solve the problem?

Solution

A)

As they are independent,

P(both solve) = P(first solves) P(second solves) = (1/3)(3/4) = 1/4 [answer]

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b)

P(at least one wil solve) = 1 - P(none will solve)

= 1 - P(first will not solve) P(second will not solve)

= 1 - (1-1/3)(1-3/4)

= 5/6 [answer]