Question

42. A class has 12 girls and 10 boys A hat contains the names of all the students in the class. To select representatives of the class to attend a meeting, the teacher draws two names from the hat without replacing the first name. a. Find P(two girls). b. Find P(two boys). e. Find P(boy then girl). d. Find P(girl then boy). e. Predict the sum of the probabilities in parts (a)-(d). Check to see that the sum agrees with your prediction.

Answer 1

a) Probability of selecting two girls from the two picks without replacing is: 0.2857

b) Probability of selecting two boys from the two picks without replacing is: 0.1948

c) Probability of a boy and then girl is: 0.2597

d) Probability of a girl and then boy is: P(girl then boy) = 0.2597

How to solve conditional probability?

We are told that:

Number of girls in class = 12

Number of boys in class = 10

Total number of people in class = 22

a) Probability of selecting two girls from the two picks without replacing is: (12/22) * (11/21)

= 0.2857

b) Probability of selecting two boys from the two picks without replacing is: (10/22) * (9/21)

= 0.1948

c) Probability of a boy and then girl is:

P(boy then girl) = (10/22) * (12/21)

= 0.2597

d) Probability of a girl and then boy is:

P(girl then boy) = (12/22) * (10/21) = 0.2597

Answer 2

To find the probabilities in different scenarios of selecting students from a class, we calculate the probabilities step by step and predict the sum of all probabilities. The probabilities are calculated using the concept of conditional probability and without replacement.

Step-by-step explanation:

Let's analyze each part of the question step by step:

a. To find the probability of selecting two girls, we need to calculate the probability of selecting one girl and then another girl without replacement. The probability of selecting one girl from 12 girls is 12/22. After one girl is selected, there are 11 girls left out of 21 students. The probability of selecting another girl is 11/21. So, the probability of selecting two girls is (12/22) * (11/21).

b. Similarly, the probability of selecting two boys is (10/22) * (9/21).

c. To find the probability of selecting a boy first and then a girl, we first calculate the probability of selecting a boy from 10 boys, which is 10/22. After one boy is selected, there are 12 girls left out of 21 students. The probability of selecting a girl is 12/21. So, the probability of boy then girl is (10/22) * (12/21).

d. To find the probability of selecting a girl first and then a boy, we first calculate the probability of selecting a girl from 12 girls, which is 12/22. After one girl is selected, there are 10 boys left out of 21 students. The probability of selecting a boy is 10/21. So, the probability of girl then boy is (12/22) * (10/21).

e. The sum of the probabilities in parts (a)-(d) can be predicted using the probability of selecting either two girls, two boys, boy then girl, or girl then boy, which covers all possible outcomes. The sum would be (12/22) * (11/21) + (10/22) * (9/21) + (10/22) * (12/21) + (12/22) * (10/21).