There are two traffic lights on the route used by a certain individual to go fro

Question

There are two traffic lights on the route used by a certain individual to go from home to work. Let E denote the event that the individual 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) = 0.4 and P(E F) = 0.14 What is the probability that the individual must stop at least one light; that is, what is the probability of the event P(E F)? What is the probability that the individual doesn't have to stop at either light? What is the probability that the individual must stop at exactly one of the two lights? What is the probability that the individual must stop just at the first light?

Explanation / Answer

ans=

a)
P(E F) = P(E) + P(F) - P(E F)
= 0.2 + 0.4 - 0.14
= 0.46

b)
1- P(E F) = 1- 0.46 = 0.54

c)
P( E F') + P( E' F)
= (0.2)(1-0.4) + (1-0.2)(0.4)
= 0.44

d)
P(E) = P( E F) + P ( E F')
= (0.2)(0.4) + (0.2)(1-0.4)
= 0.2

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