164335
AssignmentMultiple Choice

The Multiplication Rule for Dependent Events

Question 164335 • PISD-Statistics B 4th GP

There are 36 students on the debate team at a school. There are 6 seniors, 12 juniors, 10 sophomores, and 8 freshmen on the team. The coach is going to select 4 students at random to participate in the next debate. Calculate the probability that all 4 students are sophomores.

Answer
A
0.0036
B
0.0060
C
0.0084
D
0.2778

Explanation

For all 4 selected students to be sophomores, the successive probabilities are 10/36, 9/35, 8/34, and 7/33, since each selection reduces the number of sophomores and students remaining. Multiplying gives about 0.003565, which rounds to 0.0036. Therefore, the correct choice is A, 0.0036.

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