Question

Janice knows she can expect to get a given step in an algebra problem correct 95% of the time. She does 100 problems, each with 4 steps. In how many problems can she expect to get all 4 steps correct?

Answer 1

Janice can expect to get all 4 steps correct in approximately 81 out of 100 problems, by calculating the probability of getting all steps right in one and multiplying it by the total number of problems.

Step-by-step explanation:

To calculate how many problems Janice can expect to get all 4 steps correct, we can use probability multiplication for independent events. The probability of Janice getting one step correct is 95% or 0.95. Because each step is an independent event, the probability of Janice getting all 4 steps correct in a single problem is (0.95)^4. To find the expected number of problems with all 4 steps correct out of 100 problems, we multiply this probability by 100.

Calculating this, we have (0.95)^4 ≈ 0.8145 (rounded to four decimal places). So, the expected number of problems with all steps correct is 0.8145 × 100 ≈ 81.45. Since the expected value represents an average, in practice, she can expect to get all 4 steps correct in approximately 81 problems.