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All human blood can be "ABO-typed" as one of O,A, B, or AB, but the distribution of thetypes varies a bit among groups of people. Here is the distributionof blood types for a randomly chosen person in the United States.Blood type O A B ABU.S. probability 0.46 0.41 0.12 0.01Choose a married couple at random. It is reasonable to assume thatthe blood types of husband and wife are independent and follow thisdistribution.a. What is the probability that the wife has type A and the husbandhas type B?b. What is the probability that one of the couple has type A blood andthe other has type B?

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Answer:

(a) 0.0492

(b) 0.0984

Step-by-step explanation:

The probability distribution of blood type in the US is:

[tex]\begin{array}{cc}Type&Probability\\O&0.46\\A&0.41\\B&0.12\\AB&0.01\end{array}[/tex]

(a) The probability that the wife has type A and the husband has type B is:

[tex]P(w=A\ and\ h=B) =0.41*0.12\\P(w=A\ and\ h=B) =0.0492[/tex]

(b) The probability that one of the couple has type A blood and the other has type B is given by the probability that the wife has type A and the husband has type B added to the probability that the wife has type B and the husband has type A.

[tex]P= P(w=A\ and\ h=B) + P(w=B\ and\ h=A)\\P=0.41*0.12+0.12*0.41=0.0984[/tex]

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