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Numerade Educator

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Problem 83 Medium Difficulty

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

$$\begin{array}{cccc}{A} & {B} & {A B} & {0} \\ {40} & {11} & {.04} & {.45}\end{array}$$

Assuming that the phenotypes of two randomly selected individuals are independent of each other, what is the probability that both phenotypes are $O ?$ What is the probability that the phenotypes of two randomly selected individuals match?

Answer

.1936, .3816

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Video Transcript

so using sub scripts to differentiate between the selected individuals, we have that probably one in your section 02 is equal to the probability of one times probability of 02 which is equal to a 0.45 times 0.45 which is 0.20 25 And hence the probably that two individuals match is going to be equal to the property of the one intersect. A two plus two, probably of B one Intersect be too, plus the probability of a B one intersect, maybe two, plus the probability of Owen Intersect boat too. So that comes out 2.4 squared was 0.11 square. This 0.404 squared this 0.45 squared, which is 0.37 62 So this is a probably that two individuals match