Question

A group of 40 students from your school is part of the audience for a tv game show. The total number of people in the audience is 150. What is the theoretical probability of 5 students from your school being selected as contestants out of 8 possible spots

Answer 1

Answer:

2.7% theoretical probability of 5 students from your school being selected as contestants out of 8 possible spots

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the students are picked is not important, which means that the combinations formula is used to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

Desired outcomes:

5 from your school, from a group of 40.

3 from others schools, from a group of 150-40 = 110. So

$D = C_{40,5}C_{110,3} = \frac{40!}{5!(40-5)!}\frac{100!}{3!(100-3)!} = 142011286560$

Total outcomes:

8 students, from a group of 150. So

$T = C_{150,8} = \frac{150!}{8!(150-8)!} = 5.2572114 \times 10^{12}$

Probability:

$p = \frac{D}{T} = \frac{142011286560}{5.2572114 \times 10^{12}} = 0.0270$

2.7% theoretical probability of 5 students from your school being selected as contestants out of 8 possible spots

Answer 2

The theoretical probability of 5 students from the school being selected as contestants out of 8 possible spots is 2.7%.

What is theoretical probability?

Theoretical probability of an event is the ratio of number of favorable outcome to the total expected number of outcome of that event.

A group of 40 students from your school is part of the audience for a tv game show. The total number of people in the audience is 150.

The number of people from other group is,

$150-40=110$

The theoretical probability of 5 students from your school being selected as contestants out of 8 possible spots has to be found out.

• For 5 students in the school of 40 students,

          $^5C_{40}$

• For 3 students in the 110 audience,

        $^3C_{110}$

• Total outcome for 8 spots for 150 audiences,
• $^8C_{150}$

Thus, the theoretical probability is,

$P=\dfrac{^5C_{40}\times ^3C_{110}}{^8C_{150}}\\P=0.0270\\P=2.7\%$

Hence, the theoretical probability of 5 students from the school being selected as contestants out of 8 possible spots is 2.7%.

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