MrDaberoni
Answered

A four-person committee is chosen from a group of eight boys and six girls.


If students are chosen at random, what is the probability that the committee consists of all boys?

A4/1001

B.15/1001


C.70/1001


D.931/1001

Verified Answer :

The correct answer is:

C) 70/1001

Explanation:

Choosing 4 boys from a total of 8 boys is a combination of 8 taken 4 at a time:

\(_8C_4=\frac{8!}{4!4!}=70\)

Since they are all boys, we are choosing 0 girls from 6:

\(_6C_0=\frac{6!}{0!6!}=1\)

Choosing 4 students from 6+8=14 total students is a combination of 14 people taken 4 at a time:

\(_{14}C_4=\frac{14!}{4!10!}=1001\)

This gives us a probability of 70(1)/1001 = 70/1001.

If students are chosen at random, the probability that the committee consists of all boys 70/1001.

What is the probability?

Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

Choosing 4 boys from a total of 8 boys is a combination of 4 taken at a time

\(^{8}C_4=8! / 4!4!\)

= 70

Since they are all boys, we are choosing 0 girls from 6

\(^{6}C_0=1\)

Choosing 4 students from 14 total students is a combination of 4 taken at a time

\(^{14}C_4=14! / 10!4!\)

= 1001

The probability that the committee consists of all boys

= 70/1001.

Learn more about probability here;

https://brainly.com/question/11234923

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