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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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Omoteshosegun

Answer:

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

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