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 exactly by one of them
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 E: The problem is solved exactly by one of them.
∴ P(E) = P(A' ∩ B) ∪ P(A ∩ B')
= P(A')·P(B) + P(A)·P(B')
= `(3/5 xx 1/4) + (2/5 xx 3/4)`
= `3/20 + 6/20`