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Apr 30'23
Exercise
Events [math]E[/math] and [math]F[/math] are independent. [math]\operatorname{P}[E] = 0.84[/math] and [math]\operatorname{P}[F] = 0.65[/math].
Calculate the probability that exactly one of the two events occurs.
- 0.056
- 0.398
- 0.546
- 0.650
- 0.944
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
Apr 30'23
Solution: B
If E and F are independent, so are E and the complement of F. Then,
[[math]]\operatorname{P}(\textrm{exactly one}) = \operatorname{P}( E ∩ F^c ) + \operatorname{P}( E^c ∩ F ) = 0.84(0.35) + 0.16(0.65) = 0.398. [[/math]]
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.