Answer to Question #99088 in Statistics and Probability for Sandhya

Question

A boy goes to his 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. given that he walks to the school on particular Tuesday,find the probability that he will go to the school by bus on Thursday of the week

Answer 1

It is given that he walks to school on a particular Tuesday, then we need to find the probability that he will go by bus on Thursday.

So now, we can have two cases.

$Case1:$ He will walk on Wednesday too.

Now, it is given that if one day he walks to school, then the probability that he go by bus on next day is 2/5.

So, if one day he walks to school, then the probability that he will go to school by walk on next day too will be $1-(2/5)=3/5$

So, the probability that he will walk on Wednesday given that he walked on previous day too will be equal to $3/5$

And now the probability that he will go by bus on Thursday will be equal to $2/5$ because he walked on previous day.

So, by multiplication theorem, the probability that he will go by bus on Thursday, given that he walks on Tuesday will be equal to $(3/5)*(2/5)=6/25$

$Case2:$ He will go by bus on Wednesday

Probability that he will go by bus on Wednesday given that he go by walk on Tuesday will be equal to $2/5$

Now, the probability that he go by bus on Thursday assuming he go by bus on Wednesday will be equal to $7/10$

So by multiplication theorem probability that he go by bus on Thursday, given that he walks on Tuesday will

be equal to $2/5)∗(7/10)=7/25$

Now combining both the cases by addition theorem, we can find the probability that he go by bus on Thursday given that he go by walk on Tuesday, which will be equal to $(6/25)+(7/25)=13/25$