There are 7 men and 3 women on a coed volleyball team. Two of them will be randomly selected to play in a two-person-team tournament in Santa Cruz. You might wish to sketch a tree diagram on scratch paper to help answer the following. Express your answers as fractions as you find the probability that the two selected students are...
a) both men.
b) one man and one woman.
c) both women.
d) the same gender.
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a) To find the probability that both students selected are men, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of outcomes = Total number of ways to select 2 students out of 10 = 10C2 = 45
Number of favorable outcomes = Total number of ways to select 2 men out of 7 = 7C2 = 21
Therefore, the probability that both students selected are men is 21/45 or 7/15.
b) To find the probability that one student selected is a man and the other is a woman, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of outcomes = Total number of ways to select 2 students out of 10 = 10C2 = 45
Number of favorable outcomes = (Total number of ways to select 1 man out of 7) * (Total number of ways to select 1 woman out of 3) = 7C1 * 3C1 = 7*3 = 21
Therefore, the probability that one student selected is a man and the other is a woman is 21/45 or 7/15.
c) To find the probability that both students selected are women, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of outcomes = Total number of ways to select 2 students out of 10 = 10C2 = 45
Number of favorable outcomes = Total number of ways to select 2 women out of 3 = 3C2 = 3
Therefore, the probability that both students selected are women is 3/45 or 1/15.
d) To find the probability that the selected students are of the same gender, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of outcomes = Total number of ways to select 2 students out of 10 = 10C2 = 45
Number of favorable outcomes = (Total number of ways to select 2 men out of 7) + (Total number of ways to select 2 women out of 3) = 7C2 + 3C2 = 21 + 3 = 24
Therefore, the probability that the selected students are of the same gender is 24/45 or 8/15.
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