Everyday, Rohan learns either football or cricket. If he play football one day, he has a 0.6 probability of playing cricket in the following day. If he play cricket one day, he has a probability of 0.4 on playing football the next day. What is the probability that Rohan will play football on Wednesday given that he play football on Monday? 0.24 0.36 0.4 0.6
Question
Everyday, Rohan learns either football or cricket. If he play football one day, he has a 0.6 probability of playing cricket in the following day. If he play cricket one day, he has a probability of 0.4 on playing football the next day. What is the probability that Rohan will play football on Wednesday given that he play football on Monday? 0.24 0.36 0.4 0.6
Solution
To solve this problem, we need to consider two scenarios: Rohan playing football on Tuesday and Rohan playing cricket on Tuesday.
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If Rohan plays football on Tuesday, the probability of him playing football on Wednesday is 0.4 (since the problem states that if he plays football one day, he has a 0.4 probability of playing football the next day). The probability of him playing football on Tuesday given that he played football on Monday is also 0.4. Therefore, the combined probability for this scenario is 0.4 * 0.4 = 0.16.
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If Rohan plays cricket on Tuesday, the probability of him playing football on Wednesday is 0.4 (since the problem states that if he plays cricket one day, he has a 0.4 probability of playing football the next day). The probability of him playing cricket on Tuesday given that he played football on Monday is 0.6. Therefore, the combined probability for this scenario is 0.6 * 0.4 = 0.24.
To find the total probability of Rohan playing football on Wednesday given that he played football on Monday, we add the probabilities of the two scenarios together: 0.16 + 0.24 = 0.4.
So, the probability that Rohan will play football on Wednesday given that he played football on Monday is 0.4.
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