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.

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.