Medical records show that 40% of all persons affected by a certain viral illness recover. Ten people with this illness were selected at random and injected with the vaccine. (Round all answers to 4 decimal places)

a. What is the probability that eight out of the ten people recover?

Answer:

Given:

Probability of success $(p)=0.40$ and Sample size $(n)=10$

→ The probability that eight out of the ten people recover?

$P(x=8)=(\genfrac{}{}{0ex}{}{n}{x})\cdot p^x\cdot (1–p{)}^{n–x}=(\genfrac{}{}{0ex}{}{10}{8})\cdot {0.4}^8\cdot (1–0.4{)}^{10–8}=0.010617\approx 0.0106$