There are two traffic lights on Darlene's route from home to work. Let E denote the event that Darlene must stop at the first light, and define the event F in a similar manner for the second light. Suppose that P(E) = 0.2, P(F) = 0.3, and P(E ∩ F) = 0.13. (a) What is the probability that Darlene must stop at at least one light; that is, what is the probability of the event P(E ∪ F)? (b) What is the probability that Darlene doesn't have to stop at either light? (c) What is the probability that Darlene must stop at exactly one of the two lights?
There are two traffic lights on Darlene's route from home to work. Let E denote the event that Darlene must stop at the first light, and define the event F in a similar manner for the second light. Suppose that P(E) = 0.2, P(F) = 0.3, and P(E ∩ F) = 0.13. (a) What is the probability that Darlene must stop at at least one light; that is, what is the probability of the event P(E ∪ F)? (b) What is the probability that Darlene doesn't have to stop at either light? (c) What is the probability that Darlene must stop at exactly one of the two lights?
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.8: Probabilities Of Disjoint And Overlapping Events
Problem 2C
Related questions
Question
There are two traffic lights on Darlene's route from home to work. Let E denote the event that Darlene must stop at the first light, and define the event F in a similar manner for the second light. Suppose that
P(E) = 0.2,
P(F) = 0.3,
and
P(E ∩ F) = 0.13.
(a)
What is the probability that Darlene must stop at at least one light; that is, what is the probability of the event
P(E ∪ F)?
(b)
What is the probability that Darlene doesn't have to stop at either light?
(c)
What is the probability that Darlene must stop at exactly one of the two lights?
(d)
What is the probability that Darlene must stop just at the first light? (Hint: How is the probability of this event related to
P(E)
and
P(E ∩ F)?
A Venn diagram might help.)Expert Solution
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