A representative of a market research firm contacts consumers by phone in order to conduct surveys. The specific consumer contacted by each phone call is randomly determined. The probability that a phone call produces a completed survey is 0.25.

Calculate the probability that more than three phone calls are required to produce one completed survey.

• 0.32
• 0.42
• 0.44
• 0.56
• 0.58

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: B

For there to be more than three calls before one completed survey all that is required is the first three calls not result in a completed survey. This probability is (1 − 0.25)³ = 0.42.

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.