Ap Statistics Solutions To Packet 6 - Probability The Study Of Randomness Worksheet With Answers Page 12
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21HW #39
46- 48, 50, 51, 53, 55, 57, 61
6.46 PROSPERITY AND EDUCATION Call a household prosperous if its income exceeds
$100,000. Call the household educated if the householder completed college. Select an American
household at random, and let A be the event that the selected household is prosperous and B the event
that it is educated. According to the Census Bureau, P(A) = 0.134, P(B) = 0.254, and the joint
probability that a household is both prosperous and educated is P(A and B) = 0.080. What is the
probability P(A or B) that the household selected is either prosperous or educated?
P(A or B) = P(A) + P(B) − P(A and B) = 0.134 + 0.254 − 0.080 = 0.308.
6.47 Draw a Venn diagram that shows the relation between events A and B in Exercise 6.46. Indicate
each of the following events on your diagram and use the information above to calculate the
probability of each event. Finally, describe in words what each event is.
(a) P(A and B)
{A and B} represents both prosperous and educated. P(A and B) = 0.080.
C
C
(b) P(A and B
)
{A and B
} represents prosperous but not educated.
C
) = P(A) − P(A and B) = .134 − .080 = .054.
P(A and B
C
C
(c) P(A
and B)
{ A
and B} represents not prosperous but educated.
C
and B) = P(B) − P(A and B) = .254 − .080 = .174.
P(A
C
C
C
C
(d) P(A
and B
)
{ A
and B
} represents neither prosperous nor educated.
C
C
) = 1 − (.054 + .080 + .174) = 1 − .308 = .692.
P(A
and B
12
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