Assume the probability of snow on any particular day in Laramie during February

Question

Assume the probability of snow on any particular day in Laramie during February is 7%.

a) Assuming the weather on each day in Laramie IS independent, what is the probability it will snow on the first Saturday AND on that Sunday?
Use 4 decimal places


b) If you do NOT assume the weather each day is independent (meaning if it snows on Saturday that increases the probability of having snow on Sunday) what is the probability it will snow on the first Saturday AND on that Sunday?
Use 4 decimal places

a-0.07

b-0.0049

c- 0.1351

d-0.9951

e-0.8649

f-0.14

g-There is no way to know

c) Assuming the weather IS independent again, what is the probability of snow on the first Saturday OR that Sunday?
Use 4 decimal places

Explanation / Answer

Answers to questions asked:
(a) 0.0049

(b) Correct option: (g) There is no way to know

(c) 0.1351

EXPLANATION:

(a) Let

A = Snow on first Saturday

B = Snow on that Sunday

Given:

P(A) = 0.07

P(B) = 0.07

A & B are independent.

So,

P(A AND B) = P(A) P(B) = 0.07 X 0.07 = 0.0049

(b) If A and B are not independent:
P(A AND B) = P(A) P(B/A)

But, P(B/A) is not given,

So, correct option:

(g) There is no way to know.

(c) P(A OR B) = P(A) + P(B) - P(A AND B)

                      = 0.07 + 0.07 - 0.0049

                     = 0.1351

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