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According to data from the state blood program, 40 percent of all individuals have group A blood. If six individuals give blood, find the probability that exactly three of the individuals have group A blood.

User Gitter
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Answer: 0.27648

Explanation:

Given : The proportion of all individuals have group A blood : p=0.040

Total individuals give blood : n= 6

Let X be the number of individuals have group A blood.

Since all individual are independent of each other.


X\sim Bin(n=6, p=0.40)

Formula :
P(X=x)=^nC_xp^x(1-p)^(n-x) , where n= sample size , p = probability of getting success in each trial.

The probability that exactly three of the individuals have group A blood. :


P(x=3)= ^6C_3(0.40)^3(1-0.4)^3\\\\= (6!)/(3!3!)*(0.40)^3(0.60)^3\\\\=0.27648

The probability that exactly three of the individuals have group A blood. is 0.27648

User Rajeev Kumar
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