91Ó°ÊÓ

Let A be the event that antigen-A will react with the given person’s blood.

Let B be the event that antigen-B will react with the given person’s blood

The probability of type O blood is:

\(\Pr \left( {Otype} \right) = 0.5\)

The probability of type A blood is:

\(\Pr \left( {Atype} \right) = 0.34\)

The probability of type B blood is:

\(\Pr \left( {Otype} \right) = 0.12\)

Therefore, the probability of AB blood type is:

\(\Pr \left( {ABtype} \right) = 0.04\)

The probability that antigen-A will react with this person’s blood is:

\(\begin{aligned}{}\Pr \left( A \right) &= \Pr \left( {Atype} \right) + \Pr \left( {ABtype} \right)\\ &= 0.34 + 0.04\\ &= 0.38\end{aligned}\)

Since antigen-A reacts with blood type A or blood type AB,

The probability that antigen-A will react with this person’s blood is:

\(\Pr \left( A \right) = 0.38\)

The probability that antigen-B will react with this person’s blood is:

\(\begin{aligned}{}\Pr \left( A \right) &= \Pr \left( {Btype} \right) + \Pr \left( {ABtype} \right)\\ &= 0.12 + 0.04\\ &= 0.16\end{aligned}\)

Since antigen-B reacts with blood type B or blood type AB,

The probability that antigen-B will react with this person’s blood is:

\(\Pr \left( B \right) = 0.16\)

The probability that both antigens will react with this person’s blood is:

\(\begin{aligned}{}\Pr \left( {A \cap B} \right) &= \Pr \left( {ABtype} \right)\\\Pr \left( {A \cap B} \right) &= 0.04\end{aligned}\)

Antigen-A and antigen-B both react with blood type AB only,