Mathematics: The Red Cross regularly conducts Blood Drives throughout the country. They often conduct emergency drives when they are in need of rare blood types. Blood type AB-negative is the rarest type of blood. Only 0.6% of us have this type of blood. Suppose a random sample of 30 blood donors is obtained. What is the probability that at least 2 of them have blood type AB-negative? a. 0.013 b. 0.999 c. 0.986 d. 0.014 e. 0.0008

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The Red Cross regularly conducts Blood Drives throughout

SweetBriar

12.02.2022

The probability is $P( X \ge 2) = 0.986$

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

$X \~ \ \ \ B(n , p)$

and the probability distribution function for binomial distribution is

$P(X = x) = ^{n}C_x * p^x * (1- p)^{n-x}$

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

$P( X \ge 2) = 1 - P( X < 2 )$

$P( X \ge 2) = 1 - [P( X = 0 ) + P( X = 1 ) ]$

=> $P( X \ge 2) = 1 - [1 * 1 * 0.8348 ] + [30 * 0.006 * 0.83986 ]$

=> $P( X \ge 2) = 0.986$

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