What is the probability that the lead singer's voice will be fine at the band's next gig, which is 2 weeks from now?

Question

there is a 4% chance that a band's lead singer's voice isnt working on any given day. This band has played 19 gigs so far this year, and at each of these the lead singer's voice has been fine. What is the probability that the lead singer's voice will be fine at the band's next gig, which is 2 weeks from now? Assume she never is sick for more than 7 consecutive days, and the interval between bouts of illness is inherently unpredictable.

Answer 1

0.96

The probability is fixed. It's irrelevant that she has been well for 19 gigs so far as the probability of being sick on one day isn't affected by whether she was well or sick the previous day

Mike