blood distribution probabilities

[bpilgrim]

hello. im new to the board and have a question for you. any kind of help would be greatly appreciated
my question involves different blood types and percentages of them of of the u.s. population

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


the question asks, if there is a blood drive at the local public health centre, what is the probability that the first 3 people in the line that came to donate are of the same blood type?

what is my first step in solving this? the question doesnt say how many people are in the line. does this information matter though?

 

[soroban]

Hello, bpilgrim!

Welcome aboard!

My question involves different blood types and percentages of them of of the US population

. . \(\displaystyle \begin{array}{cc}\text{type A:} & 42\% \\ \text{type B:} & 10\% \\ \text{type AB:} & 4\% \\ \text{type O:} & 44\% \end{array}\)


If there is a blood drive at the local public health centre,
what is the probability that the first 3 people in line are of the same blood type?

What is my first step in solving this?
The question doesn't say how many people are in the line.
Does this information matter though? . . . . no

We assume that the percentages are constant for each person who donates.

So we have:

. . \(\displaystyle \begin{array}{ccc} P(\text{3 As}) &=& (0.42)^3 \\ P(\text{3 Bs}) &=& (0.10)^3 \\ P(\text{3 ABs}) &=& (0.04)^3 \\ P(\text{3 Os}) &=& (0.44)^3 \end{array}\)


\(\displaystyle \text{Then: }\;P(\text{3 same type}) \;=\;P\bigg(\text{[3 As] or [3Bs] or [3 ABs] or [3 Os]}\bigg)\)

. . . . . . . . . . . . . . . . \(\displaystyle =\; P(\text{3 As}) + P(\text{3Bs}) + P(\text{3 ABs}) + P(\text{3 Os})\)


Got it?

 

[bpilgrim]

ohh alright.

so,I should end up with this:

= 0.074088 + 0.001 + 0.000064 + 0.085184

= .160336 or 16%

the probability that the first 3 people are of the same type is 16%


thanks