Blood types probabilities problem

[Mspike6]

Hey .

i have a question about Probabilit. it's pretty easy but very time consuming, and so am pretty sure their must be anther way to do it. so if someone know anther way to do this question please go ahead and point it to me .


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

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


*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 hundredth of one percent.



my soultion would be .

a)draw sample space for the whole thing (Person 1, 2 , 3 , 4 and 5) with all the probabilities.

b) Eliminate any event which has a person with AB blood in it

c) Multiply the % of every event (except those that i eliminated) and then Add them .

Drawing the Sample space only would take atleast 30 minutes . and am pretty sure that's not the way am supposed to do it, because the exam is 2 hrs and they wouldn;t want me to spend 30 mins doing a probability question :D

Thanks guys

 

[Mark44]

Look at this as a binomial event - a person's blood type is either AB or it isn't. For a given person, P(AB blood type) = .04, and P(not AB blood type) = .96.

Now, how would you calculate the probability of 5 people not having this blood type?

 

[Mspike6]

Look at this as a binomial event - a person's blood type is either AB or it isn't. For a given person, P(AB blood type) = .04, and P(not AB blood type) = .96.

Now, how would you calculate the probability of 5 people not having this blood type?

I would say

Number of trails n = 5 (this is what am not sure of)
x = 0
p = 0.96
q=0.04

then sub. in nCk * P^x * q^n-xwhich gives me 1.0e-7 , which is 0%is that true ?

and thanks a lot Mark for trying to help me (again) :D

 

[Mark44]

1.0e-7 is not 0; it is 1.0 X 10^-7, which is 0.0000001, or 0.00001%

 

[Mspike6]

1.0e-7 is not 0; it is 1.0 X 10^-7, which is 0.0000001, or 0.00001%

Ya, but we usually write the answers to the nearest one hundredth of a percent. which makes it 0 if am not mistaken.


Thanks again :)

 

[HallsofIvy]

Ya, but we usually write the answers to the nearest one hundredth of a percent. which makes it 0 if am not mistaken.


Thanks again :)

Who is "we"? If this is something your class has been instructed to do, you should have told us that.

 

[vela]

He did actually. :)

*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 hundredth of one percent.

It would have been better, though, if he said the answer rounds to zero percent rather than it is zero percent. I know when I read that, I thought, "What?!"