An outdoor basketball tournament consists of 3 days, from 7 April to 9 April. The weather of each day in April is classified as either sunny or rainy. The probability that 1 April is rainy is 0.5. The probability that a sunny day follows a sunny day is 0.75. The probability that a sunny day follows a rainy day is 0.25. Find the probability that 3 days is sunny in the tournament period.

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Royce Moore · Accepted Answer

Step 1  Given:  - Probability of April 1 is rainy day is, P(R)=0.5.  - Probability of sunny day follows a sunny day is, P(SS)=0.75.  - Probability of sunny day follows a rainy day is, P(SR)=0.25.  The objective is to find the probability that 3 days is sunny in the tournament period.  Step 2  The Probability of April 1 is sunny day is,  P(S)=1−P(R)  =1−0.5  =0.5  It is given that, the probability of sunny day follows a sunny day is, P(SS)=0.75.  If April 1 is a sunny day, then the probability of second day as sunny is, P(S2)=0.75.  Similarly, the probability of third day as sunny is, P(S3)=0.75.  Then, the probability that 3 days is sunny in the tournament period can be calculated as,  P(S1S2S3)=0.5×0.75×0.75  =0.281  Hence, the probability that 3 days is sunny in the tournament period is 0.281.

An outdoor betball tournament consists of 3 days, from 7 April to 9

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