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.

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.

Dr. Hawk works in an allergy clinic, and his patients have the following allergies: 68 are allergic to diary products, 93 are allergic to pollen, 91 are allergic to animal fur, 31 are allergic to all three, 29 are allergic only to pollen, 12 are allergic only to dairy products, 40 are allergic to to dairy products and pollen.

A charity asked people attending a fundraiser cookout if they ate the salad, casserole or dessert. Here is the Venn diagram of the results.
Of those surveyed, how many people ate casserole, but not dessert?
(Points : 3)

2. A mini license plate for a toy car must consist of a number followed by two letters. Each letter must be a C, A or R. Each number must be a 3 or 7. Repetition of letters is permitted.
Use the counting principle to determine the number of points in the sample space.
Construct a tree diagram to represent this situation
Li

Consider the Venn Diagram attached in Word document below. The numbers in the regions of the circle indicate the number of items that belong to that region.
Determine:
1. n(A)
2. n(B)
3. P(A)
4. P(B)
5. P(A/B)
6. P(B/A)

Construct a Venn diagram and answer the following questions:
i. How many had only a zoo membership?
ii. How many had only an aquarium membership?
iii. How many belonged to either one or the other or both?
iv. How many belonged to neither?

Survey of 36 students
Students' Preference:
25 Cake
20 Ice Cream
15 pie
2 all three
1 no desserts
15 cake or ice cream
8 pie or cake
3 ice cream only
Draw a Venn Diagram that will represent the responses.

See attachment
Use a Venn diagram to determine whether...
23. In a television game show, there are five questions to
answer. Each question is worth twice as much as the previous
question. If the last question was worth $6400,
what was the first question worth?

Creating a venn diagram post survey.
Construct a Venndiagram, label your diagram clearly. Use your diagram to answer the following questions
A survey asked participants many questions. Among the questions were these two:
Do you own an Ipod? Are you over the age of 45?
33 did own an Ipod
57 were over the age of 45

Answer the following:
(A) Find the binomialprobability P(x = 6), where n = 15 and p = 0.60.
(B) Set up, without solving, the binomialprobability P(x is at most 6) using probability notation.