Answer:
a) [tex]0.58[/tex]
b) [tex]0.598[/tex]
c) [tex]0[/tex]
Explanation:
Given -
Total sample i.e n [tex]= 18[/tex]
Probability (p) [tex]= 3[/tex] % [tex]= 0.03[/tex]
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 [tex]X = 0[/tex]
[tex]P(X=0) = 0.03^0 * 0.97^{18}\\= 0.5779 = 0.58\\[/tex]
[tex]0.58[/tex]
b) At most one sample is mutated
[tex]P(X=0) = 0.58 + 0.03^1 * 0.97^{17}\\= 0.598[/tex]
c) More than half the samples are mutated.
[tex]P(X = 10) + ........+ P(X = 18) = 0[/tex]
