Question

Mrs Silverstein has 14 boys and Il girls in her

class. She must select two students at random to
serve as the class presidents What is the
probability that she will choose a boy followed by a
giri?

Answer 1

Explanation:

Here, I will instead go through the process for finding the probability of choosing two girls. Then once you understand how it was done, hopefully you will be able to answer the actual question for yourself.

• Finding the probability of choosing two girls. Let's make it simpler by starting with the probability of choosing the first girl only.

Probability of choosing the first girl. (Note: the letter chosen to represent the event is not important. Pick something that makes sense to you and be consistent)

• P(G1) = # of girls / # of total outcomes

So the number of girls we know to be 11. What is the number of total outcomes? Well a boy or a girl can be chosen, and there are 14 boys and 11 girls, for a total of 25 students.

• P(G1) = 11/ 25

Let's find the probability of choosing the second girl from here.

• P(G2) = # of girls / # of total outcomes

However, this time things have changed. We've already chosen one girl, so the number of girls remaining to choose from is reduced 11 to 10. And the total number of students to choose from is reduced from 25 to 24.

• P(G2) = 10 / 24

Now we have the probability of choosing the first girl and the probability of choosing the second girl. From here, we just need to combine them to find the probability of both things happening together. To calculate the probability of two different events occurring, you multiply the two probabilities together.

Probability of choosing two girls. Let's use T for Two girls.

P(T) = P(G1) × P(G2) = (11 /25) × (10/24)

From here you can use a calculator to find the answer. This answer can either be written as a fraction, a decimal, or a percentage.

= 0.19 = 19 / 100 = 19%