Question

Daniel is a researcher interested in studying depression in high school students. He gathers a sample from a local high school consisting of 10 male sophomores, 14 female sophomores, 14 male juniors, and 10 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? Please give your answer as a decimal proportion. Round to the nearest two decimal

Answer 1

The probability that both students randomly selected will be male sophomores is calculated by multiplying the individual probabilities: (10/48) * (9/47), resulting in approximately 0.04 after rounding.

Step-by-step explanation:

Daniel is interested in the likelihood that both students selected will be male sophomores. Since there are 10 male sophomores out of a total of 48 students (10 + 14 + 14 + 10), the probability of the first student being a male sophomore is 10/48. If the first student is a male sophomore, there are now 9 male sophomores left out of 47 total students. Therefore, the probability of the second student also being a male sophomore is 9/47. To find the total probability of both events occurring, we multiply the individual probabilities: (10/48) * (9/47), which equals approximately 0.04 after rounding to the nearest two decimals. So, the likelihood that both students selected are male sophomores is 0.04.