Final answer:
The probability that Jennie selects two B-level problems at random is approximately 0.357 or 35.7%, calculated using combinations and probability formulas.
Step-by-step explanation:
Jennie's teacher told her to select two problems from a list of two C-level problems, five B-level problems, and one A-level problem. If she selected at random, the question is asking for the probability that she selected two B-level problems. To solve this, we can use the formula for combinations and probabilities. Since there are five B-level problems, the number of ways to choose two B-level problems is given by the combination formula, which is 5 choose 2 (notated as 5C2).
There are a total of 2 + 5 + 1 = 8 problems, and Jennie needs to choose 2 problems, so the total number of ways to choose any 2 problems from the 8 is 8C2. Thus, the probability that Jennie will select two B-level problems is calculated by dividing the number of ways to choose two B-level problems by the total number of ways to choose any two problems: P(two B-level problems) = 5C2 / 8C2.
Calculating this, we get:
- 5C2 = 5! / (2!(5-2)!) = 10
- 8C2 = 8! / (2!(8-2)!) = 28
- P(two B-level problems) = 10 / 28 = 5 / 14 ≈ 0.357
So, the probability that Jennie selects two B-level problems at random is approximately 0.357 or 35.7%.