Sure, let's solve this step by step.
Given the probabilities of blood types in the United States:
- Probability of blood type O, [tex]\( P(O) = 0.58 \)[/tex]
- Probability of blood type A, [tex]\( P(A) = 0.15 \)[/tex]
- Probability of blood type B, [tex]\( P(B) = 0.02 \)[/tex]
- Probability of blood type AB, [tex]\( P(AB) = 0.25 \)[/tex]
We are asked to find the probability that a randomly chosen American does not have type O blood.
The probability that an individual does not have type O blood is given by the complement of the probability of having type O blood. In other words:
[tex]\[ \text{Probability of not having type O blood} = 1 - P(O) \][/tex]
Substituting the given value:
[tex]\[ \text{Probability of not having type O blood} = 1 - 0.58 \][/tex]
Performing the subtraction:
[tex]\[ \text{Probability of not having type O blood} = 0.42 \][/tex]
To express this probability as a percentage, we multiply by 100:
[tex]\[ \text{Probability of not having type O blood (as a percentage)} = 0.42 \times 100 \][/tex]
[tex]\[ \text{Probability of not having type O blood (as a percentage)} = 42 \% \][/tex]
Finally, rounding to the nearest [tex]\( 0.01 \% \)[/tex]:
[tex]\[ \text{Rounded probability} = 42.00 \% \][/tex]
Thus, the probability that a randomly chosen American does not have type O blood, rounded to the nearest [tex]\( 0.01 \% \)[/tex], is [tex]\( 42.00\% \)[/tex].
