Question

There are four blood types, and not all are equally likely to be in blood banks. 49% of donations are type O blood, 27% of donations are type A blood, 20% of donations are type B blood, and 4% of donations are type AB blood. A person with type A blood can safely receive blood transfusions of type O and type A blood. What is the probability that if 3 donations are made, all 3 of them can be safely used in a blood transfusion on someone with type A blood?(0.27)3 = 0.0197(0.49)3 = 0.1176(0.27)3 + (0.49)3 = 0.1373(0.27 + 0.49)3 = 0.4390

Answer 1

Given

49% type O blood

27% type A blood

20% type B blood

4% type AB blood

Then, the probability is:

$P=P\left(A\text{ blood}\right)+P\left(O\text{ blood}\right)$

Therefore:

$\begin{gathered} P=\lparen0.27)\lparen0.27)\lparen0.27)+\left(0.49\right)\left(0.49\right)\left(0.49\right) \\ P=\left(0.27\right)^3+\left(0.49\right)^3=0.1373 \end{gathered}$

Answer:

(0.27)³ + (0.49)³ = 0.1373