Probability

Question

Ms. Speegle's fourth-grade class has 13 boys and 7 girls. She randomly selects two students to return books to the library. Find the probability that the students selected are the following. (Round your answers to three decimal places.)

 

(c) a boy and a girl, order being unimportant

Answer 1

Stephanie,

 

Here's one way to approach the problem:

 

What combinations could Ms. Speegle have chosen?  Answer: Two boys, two girls or one of each (BB, GG or GnB)

 

This means that P(BB)+P(GG)+P(GnB)=1  where P(...) means probability of event in parentheses.

 

So P(GnB)=1-P(BB)-P(GG)

 

This is a good approach because P(BB) and P(GG) are perhaps intuitively easy to calculate:

 

P(BB)=probability of choosing a boy first choice times probability of choosing boy second choice since these are independent events.

 

P(BB)=(13/20) *(12/19)  Notice the denominator of the second fraction is 19 since there is 1 fewer student and similarly the numerator is decremented by 1.

 

P(GG)=(7/20)*(6/19)

 

P(GnB)=1-(13/20) *(12/19)-(7/20)*(6/19)=(19*20-156-42)/(19*20)=182/380=0.479 (3 decimal places)

 

So the probability of choosing a boy and a girl is 47.9 percent or 0.479 (3 decimal places)

 

 

The same result can be obtained by summing P(BG) and P(GB) where the order matters...

 

P(BG)+P(GB)=(13/20)*(7/19)+(7/20)*(13/19)=2*7*13/380=182/380

 

Many may prefer this method because it is slightly quicker.   The fact that both methods work is something that 

can improve your understanding.