Question

A can solve 80% of the problems given in a book and B can solve 60%. What is the probability that at least one of them will solve a problem selected at random from the book?

(a) \(\frac{12}{25}\)

(b) \(\frac{97}{100}\)

(c) \(\frac{23}{25}\)

(d) \(\frac{11}{25}\)

Answer 1

Correct option is (c) \(\frac{23}{25}\)

A → 80%  &  B → 60%

E = A solve the problem

F = B solve the problem

P(E) = \(\frac {80}{100} = \frac 8{10}\)

P(F) = \(\frac {60}{100} = \frac 6{10}\)

Required Probability, 

\(P(E\cup F ) = 1 - P(\bar E) P(\bar F)\)

\(= 1 - \left(1 - \frac 8{10}\right) \left(1 - \frac 6{10}\right)\)

\(= 1 - \left(\frac 2{10} \times \frac 4{10}\right)\)

\(= \frac 11-\frac 2{25}\)

\(= \frac{25-2}{25}\)

\(= \frac{23}{25}\)

Answer 2

8/10 + 6/10 - (8/10)(6/10) = 92/100 = 23/25

Correct answer is: (c) ²³/₂₅