Blood Types and their probabilities

[nicoledawn]

The distribution of blood types among americans is: 36% A, 14% B, 44%O and 6%AB. suppose that the blood types of married couples are independent and that both the husband and wife follow this distribution:

i)what is the probability that in a randomly chosen couple the wice has thpe B blood and the other has type A
ii)what is the probability that one of a randomly chosen couple has type A and the other has type B
iii) what is the probability that at least one of a randomly chosen couple has type O blood.

I am having a really hard time with this question, so If you could please show me how to approach these types of questions, and how to develop and answer from it I would muchly appreciate this! Thanks *hugs* :wink:

 

[tkhunny]

Expand This:

\(\displaystyle (A + B + O + AB)^{2}\)

 

[pka]

When two events are independent their joint probability is the product of the probabilities. Say \(\displaystyle W_B\) means the wife has type B, then \(\displaystyle P\(W_B H_A\) = (.14)(.36)\); that is the probability that the wife is type B and the husband is type B.

If one has type A and the other type B: \(\displaystyle \begin{array}{rcl}
P(W_B H_A \cup W_A H_B ) & = & P(W_B H_A ) + P(W_A H_B ) \\
& = & P(W_B )P(H_A ) + P(H_B )P(W_A ) \\
\end{array}\)

 

[nicoledawn]

is it possible if anyone can help me with part 3 of this question. I understand the first 2 parts now, but i cant figure out how to approach part 3.

 

[tkhunny]

You didn't expand the expression, did you? It becomes quite obvious once you look at the entire distribution. This is such a small one, why not?