SOLUTION: A boy goes to school either by bus or on foot. If one day he goes to the school by bus. Then the probability that he goes by bus the next day is 7/10. If one day he walks to school

Algebra ->  Probability-and-statistics -> SOLUTION: A boy goes to school either by bus or on foot. If one day he goes to the school by bus. Then the probability that he goes by bus the next day is 7/10. If one day he walks to school      Log On


   

Question 1162255: A boy goes to school either by bus or on foot. If one day he goes to the school by bus. Then the probability that he goes by bus the next day is 7/10. If one day he walks to school then the probability that he goes by bus the next day is 2/5.
1) Given that he walks to school on a particular Tuesday, find the probability that he will go to the school by bus on Thursday of that week.
2) Given that he boy walks to school on both Tuesday and Thursday of that week, find the probability that he will also walk to the school on Wednesday.
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Given that he walks to school on Tuesday, there are only four possible scenarios. Calculate the probability of each one.

P%28W%2CW%2CW%29+=+%283%2F5%29%283%2F5%29+=+9%2F25

P%28W%2CW%2CB%29+=+%283%2F5%29%282%2F5%29+=+6%2F25

P%28W%2CB%2CW%29+=+%282%2F5%29%283%2F10%29+=+6%2F50+=+3%2F25
P%28W%2CB%2CB%29+=+%282%2F5%29%287%2F10%29+=+14%2F50+=+7%2F25

Note you don't need to find all those probabilities to answer the questions that are asked. But since the number of cases is small, finding all of them and seeing that the sum of all the probabilities is 1 gives you some confidence that you are working the problem correctly.

1) If he walks to school on Tuesday, then the probability that he goes by bus on Thursday is P%28W%2CW%2CB%29+%2B+P%28W%2CB%2CB%29+=+6%2F25%2B7%2F25+=+13%2F25.

2) If he walks to school on both Tuesday and Thursday, then the probability that he also walks to school on Wednesday is P%28W%2CW%2CW%29+=+9%2F25.