3. Use the Axioms of Probablity to show: P(AnB) P(A)- P(AnB) A, B, and C are eve

Question

3. Use the Axioms of Probablity to show: P(AnB) P(A)- P(AnB) A, B, and C are events in sample space S. P(A) 2 0.9, P(B) 2 0.8, and P(AnBnC) -0. Show that P(C) s 0.3. 4. 5. Suppose we have the following information: There is a 60% chance that it will rain today. There is a 50% chance that it will rain tomorrow There is a 30% chance that it does not rain either day. Find the following probabilities a. The probability that it will rain today or tomorrow. b. The probability that it will rain today and tomorrow c. The probability that it will rain today but not tomorrow d. The probability that it either will rain today or tomorrow, but not both

Explanation / Answer

Please post 1 question at a time. here' the answer to the question 5. Write back in case you haven't understood any part of it

5.

Answer to the question is as follows:

P(rain today) = .60

P(rain tomorrow) = .50

P(won't rain either day) = .30

a. P(rain today or tomorrow) = 1- P(won't rain either day)

= 1-.30

= .70

b. P(rain today and tomorrow) = ?

P(rain tomorrow or today) = P(rain today)+P(rain tomorrow) - P( rain both days)

.7 = .6+.5 - P(rain both days)

P(rain both days) = .4

c. P(rain today but not tomorrow) = P(Rain today) - P(Rain both days) = .6-.4 = .2

d. P(rain either but not both days) = P(only rain today) + P(only rain tomorrow) = .6-.2+.5-.2 = .7

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