Please show steps. Thanks for your help 1. Ben drives to school for his class on

Question

Please show steps. Thanks for your help

1. Ben drives to school for his class on Monday, Wednesday, and Friday. He prefers to park in parking lot A because the walk to class is shorter. If it is sunny the probability that he finds a spot is 0.7 but if it is raining more people drive, so the probability that he finds a spot is only 0.4. Whether he finds a spot in Lot A is independent from one day to another.

a. On a sunny day, what is the probability that Ben does not find a spot in Lot A?

b. In a week that is sunny on Monday and Friday and raining on Wednesday, what is the probability that Ben does not find a spot in Lot A on any of the 3 days?

c. In a week that is sunny on Monday and Friday and raining on Wednesday, what is the probability that Ben finds a spot in Lot A on at least one of the three days?

Explanation / Answer

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a)as we can see from contigency table,

P(no spot | sunny day ) = 0.3

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b)

P(no spot on monday being sunny ) =0.3

P(no spot on friday being sunny ) =0.3

P(no spot on wednesday being rainy ) =0.6

P(Ben does not find a spot in Lot A on any of the 3 days) = 0.3*0.3*0.6 =0.054

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c)

P(Ben finds a spot in Lot A on at least one of the three days)= 1 - P(Ben does not find a spot in Lot A on any of the 3 days)

= 1 - 0.054

=0.946

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