3. (25%) The following probability model describes the number of snow storms for

Question

3. (25%) The following probability model describes the number of snow storms for Washington, D.C. for a given year:

Number of Storms

0

1

2

3

4

5

6

Probability

.25

.33

.24

.11

.04

.02

.01

a.

What is the probability of more than 2 but less than 5 snowstorms?

b.

Given this a particularly cold year (in which 2 snowstorms have already been observed), what is the conditional probability that a total of 4 or more snowstorms will be observed?

c.

What is the probability that there are 7 or more snowstorms in the year?

Number of Storms

0

1

2

3

4

5

6

Probability

.25

.33

.24

.11

.04

.02

.01

Explanation / Answer

Part (b) of the first solution is wrong!

a)

P(2 < X < 5) = P(X=3)+P(X=4) = 0.11+0.04 = 0.15

b)

P(X = 4 | X >= 2) =

P(X=4 and X>=2)/P(X>=2) =

P(X=4)/P(X>=2) =

0.04/(0.24+0.11+0.04+0.02+0.01) =

2/21 = 0.095

c)

P(X >= 7) =

1-(0.25+0.33+0.24+0.11+0.04+0.02+0.01) = 0

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