A study considered risk factors for HIV infection among intravenous drug users [11]. It found that 40% of users who had ≤ 100 injections per month (light users) and 55% of users who had > 100 injections per month (heavy users) were HIV positive. 4.54 What is the probability that exactly 3 of 5 light users are HIV positive?

Question

Mathematics

Ayden Erickson

23 March, 22:44

A study considered risk factors for HIV infection among intravenous drug users [11]. It found that 40% of users who had ≤ 100 injections per month (light users) and 55% of users who had > 100 injections per month (heavy users) were HIV positive. 4.54 What is the probability that exactly 3 of 5 light users are HIV positive?

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Answers (1)

Know the Answer?

Savannah Lee · Answer 1

0.576

Step-by-step explanation:

For light users, given the Probability is X<100 is:

p = P (X < = 100) = 40% = 0.4

q = 1 - 0.4 = 0.6

Given n=5 and x=3, we use Bernoulli probabilty distribution

P (X=x) = nCx * (p) ^x * (q) ^n-x

P (X=3) = 5C3 * (0.4) ³ * (0.6) ²

= 10 * 0.16 * 0.36

= 0.576