When asked about their driving, 56% of students say they are better than the average driver, 39% say they are an ave. driver and the rest say they are worse than ave. A pair of students are driving home together for break. What is the probability that at least one student said they were worse than average as a driver?

What I have so far is:
P(at least one student said they were worse ave. driver)
= 1 - P(no students saying they were worse than ave. driver)
= 1- (0.95????
I am confused here. Please help and show work so I can understand.

The probability that the 1st driver says equal or better than average is .95. The probability that both say better than average is .95*.95 = .9025

Ergo, the prob that at least one says worse than average is 1-.9025 = .0975

Thank you.

To find the probability that at least one student said they were worse than average as a driver, you can consider the complementary event: the probability that no student said they were worse than average as a driver.

Let's work through it step by step:

1. Calculate the probability that a single student said they were worse than average:
- Given that 56% of students say they are better than average, this means that 44% of students think they are an average or worse than average driver.
- Since the distribution of students who think they are average or worse is not specified, let's assume it is evenly distributed between being an average or worse-than-average driver.
- Therefore, the probability of a single student saying they are worse than average is 44% / 2 = 22%.

2. Calculate the probability that all students said they were better than average:
- This can be found by multiplying the probability of each student saying they are better than average since each student's response is independent.
- Since the two students are driving together, the probability that both of them said they are better than average is (0.56)^2 = 0.3136.

3. Calculate the probability that at least one student said they were worse than average:
- This is the complementary event to the probability that no student said they were worse than average.
- The probability of no student saying they were worse than average is obtained by finding the probability that all students said they were better than average (calculated in step 2).
- Therefore, P(no students saying they were worse than average) = 0.3136.

4. Finally, calculate the probability that at least one student said they were worse than average:
- P(at least one student saying they were worse than average) = 1 - P(no students saying they were worse than average)
- P(at least one student saying they were worse than average) = 1 - 0.3136
- P(at least one student saying they were worse than average) ≈ 0.6864 or 68.64%

So, the probability that at least one student said they were worse than average as a driver is approximately 0.6864 or 68.64%.