Geometry Homework

Question

Mrs. Jones surveys her class of 20 students about their siblings. In the class, 15 have a brother, 16 have a sister and 12 have both a brother and sister. What is the probability that a student has a brother of a sister?

A. 19/20

B. 15/20

C. 13/20

D. 16/20

Answer 1

Hi Leah,

We have to do 3 calculations:

1) The probability of having a brother: 15/20

2) The probability of having a sister: 16/20

So since it's and "OR" question, we add the probabilities together. 15/20 + 16/20 = 31/20

BUT WAIT, maybe some students have BOTH a sister AND a brother! So we double counted those, so have to subtract that double count.

The probability of having both a sister and a brother is 12/20.

So let's subtract (so we don't double count) and get our final answer: 31/20 - 12/20 = 19/20

A)

Answer 2

Hi Leah. The answer is a, 19/20.

Draw 2 intersecting circles. In the intersection, draw 12 sticks. In the left circle, in the large section, draw 3 sticks. This means there are 15 sticks for brothers (12+3). For the right circle, draw 4 sticks, in the large section. That means there are 16 sticks for brothers.

To get the probability that a student has a brother or sister, add all the sticks in the circles. You will count 19. That means the probability is 19/20.

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