# The probability that a student X solves a problem in dynamics is 25 and the probability that student Y solves the same problem is 14. What is the probability that the problem is solved - Mathematics and Statistics

Sum

The probability that a student X solves a problem in dynamics is 2/5 and the probability that student Y solves the same problem is 1/4. What is the probability that the problem is solved

#### Solution

Let event A: Student X solves the problem in dynamics,

event B: Student Y solves the problem in dynamics.

∴ P(A) = 2/5, P(B) = 1/4

∴ P(A') = 1 – P(A) = 1 - 2/5 = 3/5

P(B') = 1 – P(B) = 1 - 1/4 = 3/4

A and B are independent events,

A' and B' are also independent events

Let event D: Problem is solved.

Problems can be solved if at least one of the two students solves the problem.

∴ P(D) = P (at least one student solves the problem)

= 1 – P (no student solves the problem)

= 1 – P (A' ∩ B')

= 1 – P (A') P(B')

= 1 - 3/5 xx 3/4

= 1 - 9/20

= 11/20

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