A group of students from your school is part of the audience for a TV game show. The total number of people in the audience is 130. What is the theoretical probability of 3 students from your school being selected as contestants out of 9 possible contestant spots?
P(3 students selected) =
(The answer must be a integer or decimal rounded to three decimal places as needed.)
To find the theoretical probability of 3 students from your school being selected as contestants out of 9 possible contestant spots, we need to calculate the number of ways to choose 3 students from your school out of the total number of ways to choose 9 contestants out of the total audience.
The total number of ways to choose 9 contestants out of 130 audience members is given by the combination formula C(130, 9) which is calculated as follows:
C(130, 9) = 130! / (9! * (130-9)!) = 2.802075092 × 10^12
Next, we calculate the number of ways to choose 3 students from your school out of the total 9 contestants spots. This is given by the combination formula C(9, 3) which is calculated as follows:
C(9, 3) = 9! / (3! * (9-3)!) = 84
Therefore, the probability of 3 students from your school being selected as contestants is:
P(3 students selected) = C(9, 3) / C(130, 9) = 84 / 2.802075092 × 10^12 ≈ 0.000000000030
Rounded to three decimal places, the theoretical probability is approximately 0.000.
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To find the theoretical probability of 3 students from your school being selected as contestants out of 9 possible contestant spots, we need to calculate the number of ways to choose 3 students from your school out of the total number of ways to choose 9 contestants out of the total audience.
The total number of ways to choose 9 contestants out of 130 audience members is given by the combination formula C(130, 9) which is calculated as follows:
C(130, 9) = 130! / (9! * (130-9)!) = 56,087,800
Next, we calculate the number of ways to choose 3 students from your school out of the total 9 contestants spots. This is given by the combination formula C(9, 3) which is calculated as follows:
C(9, 3) = 9! / (3! * (9-3)!) = 84
Therefore, the probability of 3 students from your school being selected as contestants is:
P(3 students selected) = C(9, 3) / C(130, 9) = 84 / 56,087,800 ≈ 0.000001498
Rounded to three decimal places, the theoretical probability is approximately 0.000.