Suppose that the proportions of blood phenotypes in a particular population are as follows: A B АВ 0.46 0.15 0.02 0.37 Assuming that the phenotypes of two randomly selected individuals are independent of one another, what is the probability that both phenotypes are O? (Enter your answer four decimal places.) What is the probability that the phenotypes of two randomly selected individuals match? (Enter your answer to four decimal places.)

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Given Information:

Suppose that the proportions of blood phenotypes in a particular population are:

(a) Assuming that the phenotypes of two randomly selected individuals are independent of one another, to find the probability that both phenotypes are O:

If two events A and B are independent, then $P\left(A and B\right)=P\left(A\right)\times P\left(B\right)$

So, probability that both phenotypes O are independent and required probability is obtained as follows:

$\begin{array}{rcl}P\left(O and O\right)& =& P\left(O\right)\times P\left(O\right)\\ & =& 0.37\times 0.37\\ & =& 0.1369\end{array}$

Thus, the probability that both phenotypes of two randomly selected individuals is O is 0.1369