1. 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. Suppose we know that, P(A) = 0.134, P(B) = 0.254, and the probability that a
household is both prosperous and educated is P(A and B) = 0.080.
This question and the following two all pertain to this scenario.
A. What is Pr(A or B), that is, the probability that a household is either prosperous or
educated?
• A. .034
• B. .388
• C. .120
• D. .308
1a)Are A and B independent?
• A. Yes
• B. No
• C. Can't tell from the information provided.
• D. Neither (a) nor (b).
A:
The probability that a household is either prosperous or educated is
P(A or B) = P(A) + P(B) - P(A and B) = 0.134 + 0.254 - 0.080 = 0.308
Correct option is D.
B:
We have
P(A) * P(B) = 0.134 * 0.254 = 0.034036
Since P(A and B) is not equal to P(A)*P(B) so A and B are not independent.
Answer: B: No
1. Call a household prosperous if its income exceeds $100,000. Call the household educated if the...
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