8.4

1. Suppose that a family has 5 children. Also, suppose that the probability of having a girl (based on the gender assigned at birth) is 1/2. Find the probability that the family has the following children.

Exactly 1 girl and 4 boys.

The probability is ____.

2. Suppose that a family has 3 children. Also, suppose that the probability of having a girl (based on the gender assigned at birth) is 1/2. Find the probability that the family has the following children.

No boys.

The probability that the family has 3 children and 0 boys is _____.

3. Suppose that a family has 5 children. Also, suppose that the probability of having a boy (based on the gender assigned at birth) is 1/2.

Find the probability that the family has at least 4 boys.

The probability that the family has at least 4 boys is ___.

4. A survey finds that customers are overcharged by price scanning systems, on average, on 1.80% of items. Suppose a customer purchases 18 items. Find the following probability.

A customer is not overcharged for any item.

The probability is____.

5. According to a survey, 22.1% of credit-card-holding families in a certain area hardly ever pay off the balance. Suppose a random sample of 26 credit-card-holding families is taken. Find the probability that at least 4 families hardly ever pay off the balance.

The probability that at least 4 families hardly ever pay off the balance is_____.

6. A factory tests a random sample of 25 transistors for defects. The probability that a particular transistor will be defective has been established by past experience as 0.04. What is the probability that there are no defective transistors in the sample?

The probability that there are no defective transistors in the sample is_____.

7. According to an airline, a particular flight is on time 87% of the time. Suppose 38 flights are randomly selected and the number of on-time flights is recorded. Find the probabilities of the following events occurring.

a. All 38flights are on time

b. Between 31 and 33 flights (inclusive) are on time

a. The probability that all 38 flights are on time is_____.

b. The probability that between 31 and 33 flights, inclusive, are on time is_____.

8. A recent study found that 79% of breast-cancer cases are detectable by mammogram. Suppose a random sample of 8 women with breast cancer are given mammograms. Find the probability that all of the cases are detectable, assuming that detection in the cases is independent.

The probability that all of the cases of breast cancer are detectable is about____.

9. The probability that a birth will result in twins is 0.011. Assuming independence (perhaps not a valid assumption), what is the probability that out of 150 births in a hospital, there will be exactly 3 sets of twins?

The probability that there will be exactly 3 sets of twins is_____.

10. In a certain state, 36.9% of all community college students belong to ethnic minorities. Find the probabilities of the following results in a random sample of 10 of the community college students.

a. Exactly 3 belong to an ethnic minority.

b. Three or fewer belong to an ethnic minority.

c. Exactly 5 do not belong to an ethnic minority.

d. Six or more do not belong to an ethnic minority.

a. P(3)= ____.

b. P(three or fewer belong to an ethnic minority)= _____.

c. P(exactly 5 do not belong to an ethnic minority)=____.

d. P(six or more do not belong to an ethnic minority)= _____.

11. A study tracked a cohort of very-low-birth-weight infants for twenty years. The results of the study indicated that 73% of the very-low-birth-weight babies graduated from high school during this time period. The study also reported that 85% of the comparison group of normal-birth-weight babies graduated from high school during the same period.

(a) If 40 very-low-birth-weight babies were tracked through high school, what is the probability that at least 30 will graduate from high school by age 20?

(b) If 40 normal-birth-weight babies were tracked through high school, what is the probability that at least 30 will graduate from high school by age 20?

(a) The probability that at least 30 out of 40 very-low-birth-weight babies will graduate from high school by age 20 is ____.

(b) The probability that at least 30 out of 40 normal-birth-weight babies will graduate from high school by age 20 is ____.