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
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`