Here is the probability model for the blood type of a randomly chosen person in the United States.

Blood type O A B AB
Probability 0.28 0.35 0.1 ?

1. What is the probability that a randomly chosen American has type AB blood? Please use 2 decimal places.

2. Maria has type B blood. She can safely receive blood transfusions from people with blood types O and B. What is the probability that a randomly chosen American can donate blood to Maria? Please use two decimal places.

The probability that a randomly chosen American has type AB blood is 0.27
The probability that a randomly chosen American can donate blood to Maria is 0.03

The probability model is given as:

[tex]\mathbf{\left[\begin{array}{ccccc}Blood\ Group&O&A&B&AB\\Probability&0.28&0.35&0.1\end{array}\right] }[/tex]

(a) The probability of AB

In probability,

[tex]\mathbf{\sum P(x) = 1}[/tex] --- the sum of all probabilities is 1

So, we have:

[tex]\mathbf{P(O) + P(A) + P(B) + P(AB) = 1}[/tex]

Substitute known values

[tex]\mathbf{0.28 + 0.35 + 0.1 + P(AB) = 1}[/tex]

[tex]\mathbf{0.73 + P(AB) = 1}[/tex]

Collect like terms

[tex]\mathbf{P(AB) = 1 - 0.73}[/tex]

[tex]\mathbf{P(AB) = 0.27}[/tex]

The probability that a randomly chosen American has type AB blood is 0.27

(b) The probability of blood types O and B

In probability, "and" means product

So, we have:

[tex]\mathbf{P(O\ and\ B) = P(O) \times P(B)}[/tex]

Substitute known values

[tex]\mathbf{P(O\ and\ B) = 0.28 \times 0.1}[/tex]

[tex]\mathbf{P(O\ and\ B) = 0.028 }[/tex]

Approximate

[tex]\mathbf{P(O\ and\ B) = 0.03 }[/tex]

Hence, the probability that a randomly chosen American can donate blood to Maria is 0.03