Question

3) There is a 7% chance that a band's lead singer's voice isn't working due to illness on any given Saturday. This band has played 19 Saturday 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 Saturday gig, which is 2 weeks from now? Assume she never is sick for more than 6 consecutive days, and the interval between bouts of illness is inherently unpredictable. Hint: You DO have enough information to provide a numerical answer for this question; in other words, "Not enough information" is incorrect .

Answer 1

The probability that the lead singer's voice isn't working on any given Saturday is 7%.

Now, if she never gets sick for more than 6 consecutive days, and the interval between bouts of illness is inherently unpredictable, we can consider the following scenarios:

1. She is not sick on the upcoming Saturday (probability = 93%).

2. She gets sick in the 1st week and is still sick on the upcoming Saturday (probability = 7%).

3. She gets sick in the 2nd week and is still sick on the upcoming Saturday (probability = 7%).

4. She gets sick in the 3rd week and is still sick on the upcoming Saturday (probability = 7%).

Since these events are mutually exclusive, we can calculate the probability of scenario 1 happening, which is 93%. So, the probability that the lead singer's voice will be fine at the band's next Saturday gig, which is 2 weeks from now, is 93%.