Question

Daniel is a researcher interested in studying depression in high school students. He gathers a sample from a local high school consisting of 16 male sophomores, 18 female sophomores, 16 male juniors, and 20 female juniors. If he selects two students at random and does not replace the first student after selection, what is the likelihood that BOTH students will be male sophomores?

Answer 1

The likelihood that both students selected by Daniel will be male sophomores is about 4.97%, calculated by multiplying the probabilities of each selection without replacement.

Step-by-step explanation:

Daniel is interested in determining the likelihood that both students he selects will be male sophomores. To calculate this, we need to use the concept of probability without replacement. There are 16 male sophomores, 18 female sophomores, 16 male juniors, and 20 female juniors, giving us a total of 70 students. The probability of selecting the first male sophomore is 16/70. After selecting one male sophomore, there are 15 male sophomores left and the total number of students reduces to 69. Therefore, the probability that the second student selected is also a male sophomore is 15/69. The overall probability of both events occurring is the product of the two individual probabilities.
The probability of the first event (selecting a male sophomore first) is 16/70, and the probability of the second event (selecting another male sophomore second) is 15/69. When multiplied together, this gives:

Probability = (16/70) * (15/69) = 240/4830 which simplifies to 8/161 or approximately 0.0497. Thus, the likelihood that both students will be male sophomores is about 4.97%.