Question

Two students X and Y work independently on a particular on a problem. The probability that X will solve it is (3/4) and the probability that Y will solve it is (2/3). What is the probability that the problem will be solved? Chp-probability ,plz, plz answer

Answer 1

Given P (A solving the problem) = P (A) = 12 and P (B solving the problem) = P(B) = 13.

(i) P (the problem is solved)

P (problem is solved) = 1 - P (problem is not solved).

P (problem is not solved by A) = 1 - P (A solving the problem) = 1 - 12=12

P (problem is not solved by B) = 1 - P (B solving the problem) = 1 - 13=23

P (neither A nor B solved the problem) = P (problem not solved by A) × P (problem not solved by B) = 12 × 23 = 13

Therefore P (problem is solved) = 1 - 13=23

(ii) P (exactly one of them solves the problem)

P (exactly one of them solve the problem) = P (A solved the problem but B doesnt) + P (B solved the problem but A doesnt)

P (A solved the problem but B doesnt) = P(A) × P (B¯) = 12× 23=13

P (B solved the problem but A doesnt) = P(B) × P (A¯) = 13 × 12=16

Therefore P (exactly one of them solves the problem) = 13+16=2+16=12

Answer 2

the work would be solved either by X or Y


$= \frac{3}{4} and \frac{2}{3 } \\ = \frac{3}{4} \times \frac{2}{3} \\ = \frac{1}{2}$

here's your answer.