Question 1198912: A weather forecast for Wednesday says that the probability of snow is 0.8, the probability for hail is 0.5, and the probability of both snow and hail is 0.3.
According to the forecast, which of the following is an accurate conclusion?
A) the events of snow and hail are independent
B) the events of snow and hail are disjoint
C) either snow or hail will definitely occur
D) the events of snow and hail are complementary
Answer by ikleyn(52794)   (Show Source):
You can put this solution on YOUR website! .
A weather forecast for Wednesday says that the probability of snow is 0.8,
the probability for hail is 0.5, and the probability of both snow and hail is 0.3.
According to the forecast, which of the following is an accurate conclusion?
A) the events of snow and hail are independent
B) the events of snow and hail are disjoint
C) either snow or hail will definitely occur
D) the events of snow and hail are complementary
~~~~~~~~~~~~~~~~~
(A) They are not independent since
P(snowing & hailing) = 0.3 =/= P(snowing)*P(hailing) = 0.8*0.5 = 0.4.
(B) The events of snow and hail are NOT disjoint, since the probability of the intersection is not zero.
(C) Either snow or hail will definitely occur: YES, correct, since the sum
P(snowing OR hailing) = P(snowing) + P(hailing - P(both) = 0.8 + 0.5 - 0.3 is 1.0.
(D) The events of snow and hail are NOT complementary, since the sum of probabilities
P(snowing) + P(hailing) = 0.8 + 0.5 = 1.3 is not equal to 1.
Solved.
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