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13 Aug 2025, 12:10
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At School Y, 60% of all students are male, and 40% of all male students are transfer students. If two students at the school are selected at random from the entire student body of 25 students, what is the probability that both students will be male transfer students?
24 Aug 2025, 08:05
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Official Explanation
The number of male students at the school is 60% of 25, or .60 × 25 = 15. Of these 15 males, 40% are male transfer students. So there are 0.4 × 15 = 6 male transfer students.
To find the probability that two randomly selected students will be in this group of six out of 25, we can reason, “The first student selected must be a male transfer AND the second student must be a male transfer.” The AND requires you to multiply the two probabilities. The first probability is simply but if one male transfer student is selected, there will be only five such students remaining to choose from, out of 24 students in all.
You can find the product on your calculator, or perhaps faster by hand by cross-canceling: reduce 6 with 24 and 5 with 25 to 1/20 or .05.
The number of male students at the school is 60% of 25, or .60 × 25 = 15. Of these 15 males, 40% are male transfer students. So there are 0.4 × 15 = 6 male transfer students.
To find the probability that two randomly selected students will be in this group of six out of 25, we can reason, “The first student selected must be a male transfer AND the second student must be a male transfer.” The AND requires you to multiply the two probabilities. The first probability is simply but if one male transfer student is selected, there will be only five such students remaining to choose from, out of 24 students in all.
You can find the product on your calculator, or perhaps faster by hand by cross-canceling: reduce 6 with 24 and 5 with 25 to 1/20 or .05.
