Answer:
(a) P (X ≥ 4) = 0.972
(b) E (X) = 20
Step-by-step explanation:
Let <em>X</em> = number of people tested to detect the presence of gene in 2.
Then the random variable <em>X</em> follows a Negative binomial distribution with parameters <em>r</em> (number of success) and <em>p</em> probability of success.
The probability distribution function of <em>X</em> is:
Given: <em>r</em> = 2 and <em>p</em> = 0.1
(a)
Compute the probability that four or more people will have to be tested before two with the gene are detected as follows:
P (<em>X</em> ≥ 4) = 1 - P (<em>X</em> = 3) - P (<em>X</em> = 2)
Thus, the probability that four or more people will have to be tested before two with the gene are detected is 0.972.
(b)
The expected value of a negative binomial random variable <em>X</em> is:
The expected number of people to be tested before two with gene are detected is:
Thus, the expected number of people to be tested before two with gene are detected is 20.