Question

In a college fraternity freshmen account for 25% of its members, sophomores for 30%, juniors for 35% and seniors for 10%, respectively. Also, 40% of the freshmen, 35% of the sophomores, 15% of juniors and 3% or seniors are enrolled in the same engineering class. A fraternity member is selected at random. What is the probability that he is enrolled in the class?

Answer 1

To find the probability that a randomly selected fraternity member is enrolled in the engineering class, we multiply the percentage of each class year by the respective enrollment percentage in the class and sum them up. The result is a probability of 26.05%.

Step-by-step explanation:

The student's question involves calculating the probability that a randomly selected member of the fraternity is enrolled in a particular engineering class. To find this probability, we need to consider the percentage of each class year in the fraternity and the percentage of each class year that is enrolled in the class.

• 25% of the members are freshmen, and 40% of them are in the class.
• 30% of the members are sophomores, and 35% of them are in the class.
• 35% of the members are juniors, and 15% of them are in the class.
• 10% of the members are seniors, and 3% of them are in the class.

The total probability (P) that a randomly selected member is in the class is the sum of the probabilities for each class year:

P = (0.25 × 0.40) + (0.30 × 0.35) + (0.35 × 0.15) + (0.10 × 0.03)

Calculating these:

P = (0.10) + (0.105) + (0.0525) + (0.003)

P = 0.2605

So, the probability that the randomly selected fraternity member is enrolled in the engineering class is 0.2605, or 26.05%.