We are interested in looking at probabilities related to the weather in Chicago

Question

We are interested in looking at probabilities related to the weather in Chicago in January of 2016. During this month, there were 16 days that had a high temperature above freezing, 12 days it either snowed or rained, and 7 days it was both above freezing and rained or snowed.

a. What percentage of days did it neither snow/rain NOR hit above freezing?

            b. Are H and D mutually exclusive events? Why or why not?

            c. Are the two events, H and D, independent? Explain, using probabilities.

d. If we know that it hit above freezing, what is the probability it also rained or snowed?

View comments (1) Please answer c and d.

Explanation / Answer

(a)

Number of days that are either freezing or snow/rain : 16+12 - 7 = 21

So number of days that has neither snow/rain NOR hit above freezing is 21 / 30 = 0.7 or 70%

(b)

No becuase there are some days that are both freezing and rained or snowed.

(c)

Here we have

P(H) = 16/ 30

P(D) = 12/30

P(H and D) = 7 / 30

Since P(H and D) are not equal to P(H)P(D) so events H and D are not independent.

(d)

P(D |H) = P(H and D) / P(H) = 7 / 16 = 0.4375

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.