Question

Suppose we have a group of 10 light users and 10 heavy users. what is the probability that exactly 3 of the 20 users are hiv positive?

Answer 1

Answer: The answer is 30%.

Step-by-step explanation: Given that there is a group of 10 light users and 10 heavy users. We are to find the probability that exactly 3 of the 20 users are HIV positive.

We have the following four possible cases -

(i) All 3 are light users.

(ii) 1 is a light user and 2 are heavy users.

(iii) 2 are light users and 1 is a heavy user.

(iv) All 3 are heavy user.

Since there is a 45% chance of a light user to be HIV positive and 55% chance of a heavy user to be HIV positive, so the required probability is given by

`p\\\\=(3* 0.45+1* 0.45+2* 0.55+2* 0.45+1* 0.55+3* 0.55)/(20)\\\\=(6)/(20)\\\\=0.3\\\\=30\%.`

Thus, the probability is 30.