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The American Red Cross says that about 45% of the U.S. population has Type O blo

ID: 3135453 • Letter: T

Question

The American Red Cross says that about 45% of the U.S. population has Type O blood, 40% Type A, 11% Type B, and the rest Type AB. Make sure to show your work for each problem and keep at least three decimal places in your answer (when appropriate).

One person volunteers to give blood. What is the probability they don’t have Type O blood?

Among four potential donors (chosen at random), what is the probability that all of them have Type A blood?

Among four potential donors (chosen at random), what is the probability that none of them have Type O blood?

Among four potential donors (chosen at random), what is the probability that at least one person has Type O blood?

Explanation / Answer

American Red Cross says that about
45% has Type O blood,
40% Type A,
11% Type B,
4% Type AB

One person volunteers to give blood. What is the probability they don’t have Type O blood?
P( Don't have Type O blood) = 1 - Type O Blood = 1 - 45% = 0.55


Among four potential donors (chosen at random), what is the probability that all of them have Type A blood?
Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial

P( X = 4 ) = ( 4 4 ) * ( 0.4^4) * ( 1 - 0.4 )^0
= 0.0256



Among four potential donors (chosen at random), what is the probability that none of them have Type O blood?
P( X = 4 ) = ( 4 4 ) * ( 0.55^4) * ( 1 - 0.55 )^0
= 0.0915


Among four potential donors (chosen at random), what is the probability that at least one person has Type O blood?
P( X < 1) = P(X=0)   
= ( 4 0 ) * 0.45^0 * ( 1- 0.45 ) ^4
= 0.0915
P( X > = 1 ) = 1 - P( X < 1) = 0.9085