Question

Janet was asked the following question on her Probability Test:    Q: A class has 7 boys and 6 girls. The teacher will be picking two volunteers at random to do the recycling. What is the probability that the teacher picks one boy and one girl?

Janet's answer along with her explanation is shown below:

Well there is a 7/13 chance of picking a boy and a 6/13 chance of picking a girl- therefore, the probability of picking a boy AND a girl will be P(Boy) x P(Girl) = 7/13x6/13=42/169=25%.

Explain , in detail if you agree with her answer. Include in your answer references to independent and dependent events. If you agree that her answer is correct, explain why. If you disagree with her answers, explain what she did wrong and include the correct solution.

Answer 1

solution:

Dependent events :Two events are said to be dependent if the outcome of one event effects outcome of other event

Ex: There are 5 marbles in a bag. 4 are blue and 1 is red . If a marble is selected at random from the bag and not replaced into the bag.The chance drawing red marble will keep increasing with consective draw

Independent events: Two events are said to be independent if the outcome of one event does not effects outcome of other event

Ex : Choosing a 3 from deck of cards,replacing it and then choosing an ace as the second card.

No, I won't agree to Janet's answer.Because

Here Actually Choosing a boy and choosing a not comes under two events and they are not independent.

as after choosing a one they are not replacing .Here one can select 1 boy from boys 7C1 distinct ways and one girl in 6C1 ways  by considering as a sigle event.

The correct is:

No.of boys = 7

No.of girls =6

Total No.of students = 13

Total No.of ways to select two members from a class = n(S) = 13C2 = 78

Let A = event of selected members are 1 boy and 1 girl

n(A) = 7C1 * 6C1 = 7*6 = 42

   P(A) = n(A)/n(S) = 42/78 = 0.538 = 53.8%