Highway engineers estimate that the main highway between Lincoln and Omaha has a

Question

Highway engineers estimate that the main highway between Lincoln and Omaha has a 1% probability of being blocked in good weather, and a 5% probability of being blocked in snowy weather. The detour route, on the other hand, is a smaller road which has a 2% probability of being blocked in good weather and a 15% probability of being blocked when it snows. On a certain day, forecasters predict a 60% chance of snow.

a. Are the events that it snows and that the main highway is blocked dependent or independent?

b. Are the events that the highway is blocked and that the detour is blocked dependent or independent?

c. Find the overall probability that, on this day, the highway will be blocked (whether or not the detour is blocked).

d. Find the overall probability that, on this day, both the highway and the detour will be blocked.

e. Find the probability that, on this day, either the highway, the detour, or both will not be blocked.

Explanation / Answer

a)

thety are depedendent ;as probability of highway to be blocked is different for snowy weather then good weather

b)

they are indepndent; as they are not intercorrelated.

c)

P( highway will be blocked)=P(good weather and highway blocked)+P(sonwt weather and highway blocked)=0.4*0.01+0.6*0.05 =0.034

d)

P(both the highway and the detour will be blocked)

=P(highway blocked)*P(detour blocked)=(0.4*0.01+0.6*0.05)*(0.4*0.02+0.6*0.15)=0.003332

e)

P(at least one will not be blocked)=1-P(both blocked)=1-0.03332=0.996668

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