Question

Suppose an antibiotic has been shown to be 40% effective against common bacteria.

if the antibiotic is given to ten unrelated individuals with the bacteriaIf the antibiotic is given to five unrelated individuals with the bacteria, what is the probability that it will be effective at least three?

How do you get the answer below

For 5 unrelated individuals Now X -Bin(5,0.4) P(X>=3)=1-P(X<3)=1-(P(X=0)+P(X=1)+P(X=2))=0.31744

Answer 1

Given:

An antibiotic has been shown to be 40% effective against common bacteria.

Calculation:

Then,

The probability of success, p=40% = 40/100 = 0.4 The probability of failure, q= 1-p = 1 - 0.4 = 0.6

If the antibiotic is given to ten unrelated individuals with the bacterialf the antibiotic is given to five unrelated individuals with the bacteria.

Then, we have to find the probability that it will be effective at least three.

i.e, To find ,

But,

It is clear that, the given distribution is a binomial distribution with n=5, p=0.4 and q=0.6.

We know that, for a binomial distribution,

Then,

Hence,

The probability that it will be effective at least three is 0.31744.