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

If we were to put this in terms of a venn diagram, we would have 360 owning only brand X, 500 owning only brand Y, and 80 in between, owning both. Therefore, 80 out of the 580 owners of brand Y may have X as well, which we put into fraction form 80/580, and reduce to 4/29.

Answer 2

Answer: $\dfrac{4}{29}$

Step-by-step explanation:

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

$P(A|B)=\dfrac{P(A\cap B)}{P(B)}$

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 , $P(A)=\dfrac{420}{1000}$

$P(B)=\dfrac{580}{1000}$

$P(A|B)=\dfrac{80}{1000}$

Then , the required probability will be:-

$P(A|B)=\dfrac{\dfrac{80}{1000}}{\dfrac{580}{1000}}\\\\\\\Rightarrow P(A|B)=\dfrac{4}{29}$