Suppose that you encounter two traffic lights on your commute to school. Based o
ID: 3303088 • Letter: S
Question
Suppose that you encounter two traffic lights on your commute to school. Based on past experience, you judge that the probability is .45 that the first light will be red when you get to it, .35 that the second light will be red, and .25 that both lights will be red.
a. Produce a probability table to organize the given probabilities.
b. Determine the probability that at least one light will be red. Also name the relevant probability rule that you could use.
c. Determine the long-run percentage of days for which neither light will be red.
Explanation / Answer
a) Here we are given that P(1) = 0.45 that is the probability that the first light would be red. Similarly, P(2) = 0.35. Also we are given that P( both ) = 0.25 that is the probability that both will be red
Therefore P(1 only )= P(1) - P( both ) = 0.45 - 0.25 = 0.2 and P(2 only ) = P(2) - P(both )= 0.35 - 0.25 = 0.1
Therefore the given probabilities could be organised in a table as:
b) Probability that at least one light will be red = 1 - Probability that neither is red = 1 - 0.45 = 0.55
Therefore 0.55 is the required probability here.
This can also be solved using addition law of probability as:
P(1 or 2) = P(1)+ P(2) - P( both ) = 0.45 + 0.35 - 0.25 = 0.55
c) The long run percentage of days for which neither lights would be red is computed as:
= 100*Probability that neither of the lights would be red = 45%
therefore 45% is the required answer here.
First light red First light not red Second light red 0.25 0.1 Second light not red 0.2 1 - 0.25 - 0.1 - 0.2 = 0.45Related Questions
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