An IQ test consists of 80 multiple choice questions. A question is selected at random. Find the probability that the question number contains exactly one '7'
There are a total of 80 questions, so the probability of selecting any one question is 1/80.
To find the probability that the question number contains exactly one '7', we need to consider two cases:
1. The question number is between 1-9. There is only one digit that is a '7', so the probability is 1/10.
2. The question number is between 10-79. In this case, there are two possibilities:
a. The tens digit is a '7' and the units digit is not: 1/10 * 9/10 = 9/100
b. The units digit is a '7' and the tens digit is not: 9/10 * 1/10 = 9/100
Adding up all the probabilities:
(1/10) + (9/100) + (9/100) = 1/10 + 9/100 + 9/100 = 1/10 + 18/100 = 1/10 + 9/50 = 5/50 + 9/50 = 14/50 = 7/25
Therefore, the probability that the question number contains exactly one '7' is 7/25.