# Venn Diagram, and binomial probability problems

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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.

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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.