Probability

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frusic

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I'm having a difficult time with this question (and a couple others but I think this one is similar to the others)(bold is what I have so far)

One particular highschool encourages students to donate blood. The highschool gym is set up for this purpose. The distribution of blood types in North America is as follows:

O: 44%
B: 10%
A: 42%
AB: 4%

a) What is the probability that the first two people in the line up have the same type of blood? Express your answer to the nearest hundredth of one percent.



P(1st 2 people with same blood) / total # of possibilities

(then I did a probability tree and used the results to get the following)

= P( O, O) + P( A, A) + P(B, B) + P (AB, AB )

= P ( .44 x .44) + P( .42 x .42) + P(.10 x .10) + P(.04 x .04)

= .3816 / total # of possibilities

= .3816 / 1.378 x 100%

= 27.69 %

b) What is the probability that none of the first five people in the line up have type AB blood? Express your answer to the nearest hundreth of one percent

P (the 1st five aren't AB) = (1st five are AB) / (total number of possibilities)

I'm not sure if this equation is right, and for the (1st five are AB) do I use (.04)^5?
 
G'day, Frusic.

The total # possibilities thing is just like
P(pick a red marble) = (No. of red marbles)/(Total no. of marbles)

or better written as
P(pick a red marble) = (No. of ways to get a red marble)/(Total choices of marbles)

If we are given probabilities, this 'equation' is not usually necessary.

For the first one, stick with your tree.
P((O and O) or (A and A) or (B and B) or (AB and AB)) is what is asked.
You found this to be 0.3816 or 38.16%. Stick with it.

For the second one, P(a person is not AB) = 1 - 0.04 = 0.96. If the first five people are not AB, the first is not AB, the second is not AB and so on. Can you proceed?
 
I think so,

for part b) would it be 1 - (5 x 0.04) = 1 - .20 = .80 = 80.00% ?
 
P(AB)=0.04, then P(notAB)=0.96.
b) What is the probability that none of the first five people in the line up have type AB blood: (0.96)<sup>5</sup>!
 
5 * 0.04 = 0.2 is the probability of all five being AB.

1 - 0.2 = 0.8 is the probability of not all five having AB. That could be 1, 2, 3 or 4 of them being AB.

But we want all five not being AB.

We know the probability of a person not being AB is 0.96.

If the 'not' bit gets in the way for you,
say the probability of picking a red marble is 0.96
what is the probability the first five marbles picked are red?
 
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