Question

1. human blood types human blood is grouped into four types. the percentages of americans with each type are listed below. o 43% a 40% b 12% ab 5% choose one american at random. find the probability that this person a. has type b blood b. has type ab or o blood c. does not have type o blood

Explanation:

Step1: Probability of type B blood

The probability of an event is given by the percentage of that event. For type B blood, the percentage is \(12\%\). So the probability \(P(B)=\frac{12}{100} = 0.12\)

Step2: Probability of type AB or O blood

Use the formula \(P(A\cup B)=P(A)+P(B)\) for mutually - exclusive events.
For type AB, \(P(AB)=\frac{5}{100}=0.05\) and for type O, \(P(O)=\frac{43}{100} = 0.43\)
\(P(AB\cup O)=P(AB)+P(O)=\frac{5 + 43}{100}=\frac{48}{100}=0.48\)

Step3: Probability of not having type O blood

Use the formula \(P(\overline{A})=1 - P(A)\)
Since \(P(O)=\frac{43}{100}=0.43\), then \(P(\overline{O})=1-\frac{43}{100}=\frac{100 - 43}{100}=\frac{57}{100}=0.57\)

Answer:

a. \(0.12\)
b. \(0.48\)
c. \(0.57\)