How do I find the probability of P(O given +) for this?

Question

In the UK, 35% of the population are group A+, 8% are B+, 3% are AB+, 37% are O+, 7% are A-, 2% are B-, 1% are AB- and 7% are O-. A random sample of 9 people in the UK who are Rhesus + is taken. Find the probability that fewer than 3 are group O+.

Answer 1

(1) First I would find that if a single person Rh+ is selected at random then what is the probability they are O+ given they are Rh+.

     P(O+|Rh+)= P(O+ and Rh+)/P(Rh+) = P(O+)/P(Rh+)      since if the person is O+ they must be Rh+

                      = .37/.83=p

 

(2) Since we are sampling from a very large population we can assume a binomial distribution

      P(fewer than 3)=P(0)+P(1)+P(2)=b(0,9,p)+b(1,9,p)+b(2,9,p)

 

      b(r,n,p) represent the binomial probability of r successes in n trials with p=P(success)

 

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