Mr. Parietti needs three students to help him with a science demonstration. His class has 18 girls and and 12 boys. He randomly chooses one student who comes to the front of the room. He then chooses a second student from those still seated. What is the probability that he chooses 2 girls followed by a boy? P(girl and girl and boy)

153/1015

Step-by-step explanation:

Step 1:

Representation. This is illustrated below:

Let G represent the number of girls in the class

Let B represent the number of boys in the class

Let P(G) represent the probability of girls in the class

Let P(B) represent the probability of boys in the class.

Step 2:

Data obtained from the question:

Girl (G) = 18

Boy (B) = 12

Total = 30

Step 3:

Determination of the probability of two girls followed by a boy. This is illustrated below:

The probability that the first is a girl is given by:

P(G1) = 18/30

Probability that the second is a girl is given by:

P(G2) = 17/29

Probability that the 3rd is a boy is given by:

P(B) = 12/28

Therefore, the probability of two girls followed by a boy is given by:

P(G1G2B) = 18/30 x 17/29 x 12/28

P(G1G2B) = 3672/24360

Reduce to the lowest possible term

P(G1G2B) = 153/1015

Therefore, the probability of two girls followed by a boy is 153/1015

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