Question

Blood types All human blood can be typed as one of $O,A,B,$or $AB,$but the distribution of the types varies a bit with race. Here is the distribution of the blood type of a randomly chosen black American: Blood type: $OABAB$Probability: $0.490.270.20$?

(a) What is the probability of type AB blood? Why?

(b) What is the probability that the person chosen does not have type $AB$blood?

(c) 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 black American can donate blood to Maria?

Short answer

Part (a) The probability of type AB $0.04$

Part (b) The probability of not type $0.96$

Part (c) The probability is $0.69$

Step-by-step solution

Part (a)  Step 1. Given Information  

There is a table with all of the different types of human blood.

Part (a) Step 2. Concept Used   

An event is a subset of an experiment's total number of outcomes. The ratio of the number of elements in an event to the number of total outcomes is the probability of that occurrence.

Part (a)  Step 3. Calculation   

The probability distribution must meet the following conditions: 1) The probabilities must be $0\le p\le 1$ 2) the Sum of all the probabilities should be $1$ Using condition $2$ ,$$\begin{gathered} 0.49+0.27+0.20+P\left(B\right)=1 \\ P\left(AB\right)=1-0.96=0.04 \end{gathered}$$

Part (b) Step 1. Calculation    

Using the complementary probability formula,$$\begin{gathered} P\left(A^c\right)=1-P\left(A\right) \\ P\left(notAB\right)=1-P\left(AB\right)=1-0.04=0.96 \end{gathered}$$

Part (c) Step 1. Calculation   

$P\left(AorB\right)=P\left(A\right)+P\left(B\right)$

Using formula.

$$\begin{gathered} P\left(OorB\right)=P\left(O\right)+P\left(B\right) \\ P\left(OorB\right)=0.49+0.20=0.69 \end{gathered}$$