Question

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

Answer 1

Answer:

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

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

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

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

=>     $P( X \ge 2) = 0.986$