- a. The proportion of children who are boys is 0.46.
- b. The proportion of boys who read books for fun every day is 0.21.
- c. The proportion of girls who read books for fun every day is 0.28.
- d. It would seem more likely for a girl to read books for fun than for a boy.
- e. For a child selected at random, the probability that the child reads books for fun is 0.25.
- f. For a child selected at random, the probability that the child is a girl and reads books for fun is 0.15.
- g. For a child selected at random, the probability that the child is a girl or reads books for fun is 0.64.
- h. For a child selected at random, the probability that the child reads books for fun given that the child is a girl is 0.28.
500 children ages 5-11 were asked the following question:
"Do you read books for fun every day?"
Results are shown in the two-way table below.
Boy Girl Total
Yes 48 75 123
No 182 195 377
Total 230 270 500
What are proportions?
A proportion is the number of desired outcomes divided by the number of total outcomes.
a. Proportion of children that are boys.
There are 500 children and 230 are boys.
230/500 = 0.46
b. Proportion of boys who read books for fun every day.
There are 230 boys and 48 read books for fun every day.
48/230 = 0.21
c. Proportion of girls who read books for fun every day.
There are 270 girls and 75 read books for fun every day.
75/270 = 0.28
d. Does the likelihood of reading books for fun depend on the gender of a child?
Based on the results from b and c, it would seem more likely for a girl to read books for fun than for a boy.
e. For a child selected at random, what is the probability that the child reads books for fun?
There are 500 children and 123 read books for fun.
P = 123/500 = 0.25
f. For a child selected at random, what is the probability that the child is a girl and reads books for fun?
There are 500 children and 75 are girls who read books for fun.
P = 75/500 = 0.15
g. For a child selected at random, what is the probability that the child is a girl or reads books for fun?
There are 500 children. The favorable cases are the girls (270) plus the children who read books for fun (123) minus the girls who read books for fun (75).
P = (270 + 123 - 75)/500 = 0.64
h. For a child selected at random, what is the probability that the child reads books for fun given that the child is a girl.
There are 270 girls and 75 of them read books for fun.
P = 75/270 = 0.28
- a. The proportion of children who are boys is 0.46.
- b. The proportion of boys who read books for fun every day is 0.21.
- c. The proportion of girls who read books for fun every day is 0.28.
- d. It would seem more likely for a girl to read books for fun than for a boy.
- e. For a child selected at random, the probability that the child reads books for fun is 0.25.
- f. For a child selected at random, the probability that the child is a girl and reads books for fun is 0.15.
- g. For a child selected at random, the probability that the child is a girl or reads books for fun is 0.64.
- h. For a child selected at random, the probability that the child reads books for fun given that the child is a girl is 0.28.
Learn more about proportions here: https://brainly.com/question/25259185
