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 exactly by one of them

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#### 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 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`

= `9/20`

Concept: Independent Events

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