Question

James lives in San Francisco and works in Mountain View. In the morning, he has 333 transportation options (bus, cab, or train) to work, and in the evening he has the same 333 choices for his trip home. If James randomly chooses his ride in the morning and in the evening, what is the probability that he'll take the same mode of transportation twice?

Answer 1

number of tarnsport available=333

p(getting of same mode of transportiation twice)=1/333

Answer 2

Given :

No of options including bus , car or train James has  to  go for work in the morning = 333

No of options he has in the evening = 333

To Find :

The probability that he will take the same mode of transportation twice if he randomly chooses his ride in the morning and in the evening = ?

Solution :

Let the probability of taking any one mode of transportation be :

$P(A) = \frac{1}{333}$

So, the probability that he will take the same mode while returning ( let  this event be B  ) is  $P(\frac{B}{A})$   ( i.e. probability of B when a has happened ).

So, this is a case of conditional  probability .

Now , as B and A are independent events so :

$P(\frac{B}{A}) = P(B) = \frac{1}{333}$

So, the probability that he will take the same mode of transportation twice is $\frac{1}{333}$ .