Question

Of the 1,000 students in a local college, 420 own brand X mobile phones and 580 own brand Y mobile phones. Of these students, 80 own both brands of mobile phones. Find the probability that a student chosen at random has a brand X mobile phone given that he has a brand Y mobile phone.

Answer 1

Answer:
`(4)/(29)`

Explanation:

We know that the formula to find the conditional probability of A given that B is given by :-

`P(A|B)=(P(A\cap B))/(P(B))`

Let A be the event that students own mobile phones of Brand X and B be the event that students own mobile phones of Brand Y.

Then ,
`P(A)=(420)/(1000)`

`P(B)=(580)/(1000)`

`P(A|B)=(80)/(1000)`

Then , the required probability will be:-

`P(A|B)=((80)/(1000))/((580)/(1000))\\\\\\\Rightarrow P(A|B)=(4)/(29)`