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.

The question is incomplete, below is the complete 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 the individual needn't stop at either light?

b) What is the probability that the individual must stop at exactly one of the two lights? c) What is the probability that the individual must stop just at the first light?"

Answer:

A. 0.63

B. 0.24

C. 0.07

Step-by-step explanation:

Data given,

P (E) = 0.2, P (F) = 0.3, and P (E ∩ F) = 0.13.

From the question, we can conclude that the event are dependent, hence

a. P (needn't stop at either light) = 1 - P (Need to stop at either light)

P (EUF) ' = 1-P (EUF)

P (EUF) ' = 1 - (P (E) + P (F) - P (E ∩ F))

P (EUF) ' = 1 - (0.2+0.3-0.13)

P (EUF) ' = 1-0.37

P (EUF) ' = 0.63

b. P (must stop at exactly one of the two lights) = P (must stop at either light) - P (must stop at both lights)

P (must stop at exactly one of the two lights) = P (E u F) - P (En F)

but P (E u F) = 0.37,

P (En F) = 0.13,

P (must stop at exactly one of the two lights) = 0.37 - 0.13 = 0.24

c. P (must stop at just the first light) = P (must stop at either light) - P (must stop at the second light)

P (must stop at just the first light) = P (E u F) - P (F)

P (must stop at just the first light) = 0.37 - 0.3 = 0.07