Probability blood type

[snsdno1234567]

People with type O− blood can donate blood to all other blood groups, but they can receive type O− blood. Approximately 7% of people have type O− blood. Suppose a person needs type O− blood, and 10 people volunteer to donate blood. What is the probability that at least one of the 10 people hasO− blood?

I wanted to do 1-P(none were blood type o-)= 1-0.93= 0.07. Is this correct

 

[Dr.Peterson]

You're heading in the right direction, but you haven't taken into account the 10 people in the sample. You just got back to the 7% you were given!

 

[pka]

People with type O− blood can donate blood to all other blood groups, but they can receive type O− blood. Approximately 7% of people have type O− blood. Suppose a person needs type O− blood, and 10 people volunteer to donate blood. What is the probability that at least one of the 10 people hasO− blood?

I wanted to do 1-P(none were blood type o-)= 1-0.93= 0.07. Is this correct

People with type O− blood can donate blood to all other blood groups, but they can receive type O− blood. Approximately 7% of people have type O− blood. Suppose a person needs type O− blood, and 10 people volunteer to donate blood. What is the probability that at least one of the 10 people hasO− blood?

I wanted to do 1-P(none were blood type o-)= 1-0.93= 0.07. Is this correct

Well having \(\displaystyle 0^-\) blood is an independent event. The probability of not having it, \(\displaystyle \mathcal{P}(\neg O^-)=0.93 \)
So we have ten independent events. So how is that handled?

 

[Harry_the_cat]

No. You haven't taken into account that there are 10 volunteers. Have you learnt about binomial distributions?

EDIT: Great minds …. Dr Peterson. I actually wrote my response before I read yours!

 

[snsdno1234567]

You're heading in the right direction, but you haven't taken into account the 10 people in the sample. You just got back to the 7% you were given!

So would it be 1-(0.93)^0=0?

 

[snsdno1234567]

No. You haven't taken into account that there are 10 volunteers. Have you learnt about binomial distributions?

EDIT: Great minds …. Dr Peterson. I actually wrote my response before I read yours!

We havent got to that yet. So far just addition/ multiplication and independent/dependent.
Would it be correct if I do 0.07^10 since it is independent event

 

[Dr.Peterson]

So would it be 1-(0.93)^0=0?

You don't really mean that, do you? Where's the 10?

We havent got to that yet. So far just addition/ multiplication and independent/dependent.
Would it be correct if I do 0.07^10 since it is independent event

Not quite. Combine this with what you had before. As you said, "1-P(none were blood type o-)" ...

 

[pka]

So would it be 1-(0.93)^0=0?

@snsdno, this is a matter in reading. What the question demands is that among the ten volunteers there is at least one who is \(\displaystyle O^-\)
Now at least one is the opposite of none: \(\displaystyle 1-(0.93)^{10}\)

 

[snsdno1234567]

You don't really mean that, do you? Where's the 10?

Not quite. Combine this with what you had before. As you said, "1-P(none were blood type o-)" ...

So 0.07^10 is if all 100 were blood type O- correct?

 

[Dr.Peterson]

Correct.

So what is the actual answer?

 

[snsdno1234567]

Correct.

So what is the actual answer?

1-0.93^10

 

[pka]

1-0.93^10

If by \(\displaystyle 1-0.93^{10}\) you mean \(\displaystyle 1-(0.93)^{10}\) then yes that is correct.
Among ten unrelated people the probability that none is \(\displaystyle \mathcal{O}^-\) is \(\displaystyle (0.93)^{10}\).
Thus the probability that at least one is \(\displaystyle \mathcal{O}^-\) equal \(\displaystyle 1-(0.93)^{10}\)

 

[Steven G]

So would it be 1-(0.93)^0=0?

If there was one volunteer than the answer would be .07 but if there are 10 volunteers then the probability is 0. Do you really think this makes any sense?

 

[Dr.Peterson]

1-0.93^10

Yes; and that is 0.516. So there will be an acceptable donor a little more than half the time.