Answer:
Hence, the required probability is:
0.0210
Step-by-step explanation:
The total number of people who are inoculated=83
The probability that a person inoculated will get disease=20%=0.20
Now we are asked to find that exactly 10 of them will get the disease at some point in their lives.
This means we have to use binomial to find the probability.
We know that the probability of k successes out of the n experiments performed is given by:
[tex]P(X=k)=n_C_kp^kq^{n-k}[/tex]
where p is the probability of success.
and q=1-p is the probability of failure.
Hence, from the given question we have:
[tex]p=0.20\ ,\ q=0.80\\\\n=83\ and\ k=10[/tex]
Hence,
[tex]P(X=10)={83}_C_{10}\times (0.20)^{10}\times (0.80)^{83-10}\\\\\\P(X=10)={83}_C_{10}\times (0.20)^{10}\times (0.80)^{73}[/tex]
Hence, on solving the values we obtain:
[tex]P(X=10)=0.0210[/tex]
