Answer:
The probability is [tex] P( X \ge 2) = 0.986 [/tex]
Step-by-step explanation:
From the question we are told that
The proportion people with Blood type AB-negative in the world is p = 0.006
The sample size is n = 30
Generally the distribution of people with Blood type AB-negative follows a binomial distribution
i.e
[tex]X \~ \ \ \ B(n , p)[/tex]
and the probability distribution function for binomial distribution is
[tex]P(X = x) = ^{n}C_x * p^x * (1- p)^{n-x}[/tex]
Here C stands for combination hence we are going to be making use of the combination function in our calculators
Generally the probability that at least 2 of them have blood type AB-negative is mathematically represented as
[tex] P( X \ge 2) = 1 - P( X < 2 ) [/tex]
[tex] P( X \ge 2) = 1 - [P( X = 0 ) + P( X = 1 ) ] [/tex]
=> [tex] P( X \ge 2) = 1 - [1 * 1 * 0.8348 ] + [30 * 0.006 * 0.83986 ] [/tex]
=> [tex] P( X \ge 2) = 0.986 [/tex]
