# Venn Diagram, and binomial probability problems

5.10 Given P(A) = .70, P(B) = .30, and P(A ∩ B) = .00, find (a) P(A ∪ B) and (b) P(A | B).

(c) Sketch a Venn diagram and describe it in words

5.16 Given P(A) = .40, P(B) = .50. If A and B are independent, find P(A ∩ B).

6.4 Pepsi and Mountain Dew products sponsored a contest giving away a Lamborghini sports car

worth $215,000. The probability of winning from a single bottle purchase was .00000884. Find

the expected value. Show your calculations clearly. (Data are from J. Paul Peter and Jerry C.

Olson, Consumer Behavior and Marketing Strategy, 7th ed. [McGraw-Hill/Irwin, 2005], p. 226.)

6.16 Calculate each binomial probability:

a. X = 2, n = 8, π = .10

b. X = 1, n = 10, π = .40

c. X = 3, n = 12, π = .70

d. X = 5, n = 9, π = .90

6.18 Calculate each binomial probability:

a. Fewer than 4 successes in 12 trials with a 10 percent chance of success.

b. At least 3 successes in 7 trials with a 40 percent chance of success.

c. At most 9 successes in 14 trials with a 60 percent chance of success.

d. More than 10 successes in 16 trials with an 80 percent chance of success.

https://brainmass.com/statistics/probability/venn-diagram-and-binomial-probability-problems-299878

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5.10 Given P(A) = .70, P(B) = .30, and P(A ∩ B) = .00, find

(a) P(A U B)

P(A U B) = P(A) + P(B) - P(A ∩ B) = 0.70+0.30-0.00=1.00

(b) P(A | B)

P(A | B) = P(A ∩ B)/P(B) =0.00/0.30=0.00

.

(c) Sketch a Venn diagram and describe it in words

In this case, Venn diagram is made up of two circles. Since the probability of P(A ∩ B) is zero, there is no overlap between the two circles. The size of the circle A is 0.70 and the size of the circle B is 0.3. The area outside the two circles represents the neither probability of neither A ...

#### Solution Summary

Solves 5 different problems on probability. Areas covered include Venn diagram, binomial probability and expected value.

Help with statistic problems

1. Graphical Analysis Are the events shown in the Venn diagram below mutually exclusive?

Please see the attachment for graph.

2. Decide if the events are mutually exclusive.

Event A: Roll a 6 on an ideal six-sided die.

Event B: Roll a 4 on an ideal six-sided die.

1

Use the table below to answer questions 3-7.

Nursing Majors The table below shows the number of male and female students enrolled in nursing at the University of Oklahoma Health Services Center for a recent semester. Find the specified probability.

Nursing Majors Non-Nursing Majors Total

Males 95 1015 1110

Females 700 1727 2427

Total 795 2742 3537

3. The student is male or a non-nursing major.

4. The student is female or a nursing major.

5. A student is not male or a nursing major.

6. The student is male or a nursing major.

7. Are the events "being male" and "being a nursing major" mutually exclusive?

Section 3.4

8. Perform the indicated calculation. 7C3

9. Experimental Group In order to conduct an experiment, 4 subjects are randomly selected from a group of 20 subjects. How many different groups of four subjects are possible? Use the information below to answer questions 10 and 11.

Area Code An area code consists of three digits.

10. How many area codes are possible if there are no restrictions?

11. How many area codes are possible if the first digit cannot be a one or a zero?

12. What is the probability of selecting an area code at random that ends with an odd

number if the first digit can't be 1 or zero?

Section 4.1

13. Determine if the random variable x is discrete or continuous. Explain your reasoning.

x represents the number of rainy days in the month of June in Portland, Oregon.

Use the frequency distribution below to answer questions 13-17.

DVDs The number of defects per batch of DVDs inspected.

Defects 0 1 2 3 4 5

Batches 95 113 87 64 13 8

14. Use the frequency distribution to construct a probability distribution.

2

15. What is the mean of the probability distribution?

16. What is the variance of the probability distribution?

17. What is the standard deviation of the probability distribution?

18. Interpret the results in the context of the real-life situation (See the interpretations in

examples 5-7 of the text for a reference showing how to do this.).

Section 4.2

Identifying binomial experiments. Use the information below to answer question

19.

Lottery A state lottery randomly chooses 6 balls numbered from 1 to 40. You choose

6 numbers and purchase a lottery ticket. The random variable represents the number

of matches on your ticket to the numbers drawn in the lottery.

19. Is this experiment a binomial experiment? Explain your answer.

Use the characteristics of the binomial distribution given below to answer questions

20-22

Suppose there is a binomial distribution with: n = 47 and p = 0:67

20. What is the mean of the binomial distribution?

21. What is the variance of the binomial distribution?

22. What is the standard deviation of the binomial distribution?

Use the characteristics of the binomial experiment below to answer questions 23-

25.

Favorite Cookie Ten percent of adults say oatmeal raisin is their favorite cookie. You

randomly select 12 adults and ask each to name his or her favorite cookie.

23. What is the probability that exactly 4 say their favorite cookie is oatmeal raisin?

24. What is the probability that at least 4 say their favorite cookie is oatmeal raisin?

25. What is the probability that less than 4 say their favorite cookie is oatmeal raisin?

See attached.

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