Question

There is a 20% probability that a person inoculated with a particular vaccine will get the disease anyway. A county health office inoculates 83 people. What is the probability that exactly 10 of them will get the disease at some point in their lives? 0.0202 0.0210 0.0412 0.9587

Answer 1

Out of 83 people 10 are being infected

Answer 2

Hence, the required probability is:

0.0210

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:

`P(X=k)=n_C_kp^kq^(n-k)`

where p is the probability of success.

and q=1-p is the probability of failure.

Hence, from the given question we have:

`p=0.20\ ,\ q=0.80\\\\n=83\ and\ k=10`

Hence,

`P(X=10)={83}_C_(10)* (0.20)^(10)* (0.80)^(83-10)\\\\\\P(X=10)={83}_C_(10)* (0.20)^(10)* (0.80)^(73)`

Hence, on solving the values we obtain:

`P(X=10)=0.0210`