Suppose that today’s weather is dependent upon the last two days. If it was sunn

Question

Suppose that today’s weather is dependent upon the last two days. If it was sunny yesterday, then it will be sunny tomorrow with probability .7. If it was rainy for the past two days, then there is a 50% chance of rain tomorrow. If it has only rained for only 1 day, then there is a 40% chance of rain tomorrow.   

If the Wed and Thursday are both rainy, what is the probability that Saturday and Sunday will both be sunny?

What percent of weekends have both sunny or both rainy days?

Assume that you are hosting an outdoor volleyball tournament. If both days are rainy, you will lose $1000. If both days are sunny, you will gain $2000. If either day is sunny, you will gain $200. What is your expected payoff for the volleyball tournament?

Explanation / Answer

Today's weather is dependent upon the last two days.

P(Tommorows weather is sunny / it was sunny yestarday) = 0.7

P(Rain tommorow / It was rainy for the past two days) = 0.5

P(Rain tommorow / It was rained for only 1 day) = 0.4

Wed and Thursday are both rainy days.

P(Rain friday / It was rainy for the past two days) = 0.5

P( Rain satarday / It was rained for only 1 day) = 0.5 * 0.4 = 0.2

P(Saturday is sunny ) = 1 - 0.2 = 0.8

P(Sunday is sunny) = 0.5 * 0.7 = 0.35

P(Saturday and sunday will both sunny) = 0.8 * 0.35 = 0.28

Percent of weekends have suuny days is 28% and Percent of weekends have rainy days is 72%

Expected pay off of volleyball tournament =0.5 * (-1000) +0.5 * (2000) +0.4 *200 = 580 $

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