Question

Samples of rejuvenated mitochondria are mutated (defective) with probability 0.11. Find the probability you need to examine at least 6 samples to find 2 samples containing mutations. Report answer to 3 decimal places.

Answer 1

The probability that more than 6 samples are needed to have 2 mutations is P=0.866.

Explanation:

This question can be analized with the binomial distribution.

We need to calculate the probability that more of 6 samples are needed to have 2 samples with mutations.

This is equal to the proability of taking 2 samples and getting one mutation or less.

Then we have a binomial distribution with n=6 and p=0.11:

`P(X\leq1)=P(0)+P(1)\\\\P(X\leq 1)=(1-p)^6+6p(1-p)^5\\\\P(X\leq 1)=0.89^6+6*0.11*0.89^5=0.497+0.369=0.866`