Question

Samples of rejuvenated mitochondria are mutated (defective) in 3% of cases. Suppose 18 samples are studied, and they can be considered to be independent for mutation. Determine the following probabilities. (a) No samples are mutated. (b) At most one sample is mutated. (c) More than half the samples are mutated.

Answer 1

a)
`0.58`

b)
`0.598`

c)
`0`

Step-by-step explanation:

Given -

Total sample i.e n
`= 18`

Probability (p)
`= 3` %
`= 0.03`

We will use binomial distribution theory for determining the probability of mutated sample

Let X be the number of mutated sample

a) No samples are mutated i.e
`X = 0`

`P(X=0) = 0.03^0 * 0.97^(18)\\= 0.5779 = 0.58\\`

`0.58`

b) At most one sample is mutated

`P(X=0) = 0.58 + 0.03^1 * 0.97^(17)\\= 0.598`

c) More than half the samples are mutated.

`P(X = 10) + ........+ P(X = 18) = 0`