Probability Practice Problems

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since 5 Feb 2008

1. Suppose the frequency of the A, B, and O alleles are 0.5, 0.2, and 0.3.

   • What is the probability of an AB individual?
     2*0.5*0.2 = 0.20

   • What is the probability of an O individual?
     0.3*0.3 = 0.09

   • What is the probability of an A individual?
     AA or Ai = 0.5*0.5 + 2*0.5*0.3 = 0.55

2. If the frequency of the Rh negative allele is 0.2, using the same A, B, and O frequencies as above

   • What is the probability of an Rh negative individual?
     0.2*0.2 = 0.04

   • What is the probability of an Rh heterozygote?
     2*0.2*0.8 = 0.32

   • What is the probability of an O negative individual?
     From your answers above, = 0.09*0.04 = 0.0036

   • What is the probability of an A positive individual?
     Pro(Positive) = Prob(++ or +-) = 0.8*0.8 + 0.32 = 0.96

     We can also obtain this by using Prob(Positive) = 1-Prob(negative) = 1-0.04 = 0.96

     Hence Prob(A and positive) = 0.55*0.96 = 0.528

3. Suppose the frequency of a particular blood type is 0.01 (one in a hundred).
   • What is the probability that we do not see this blood type if we sample 50 individual?
     Prob(none in 50) = 0.99⁵⁰ = 0.605

   • What is the probability of not seeing this blood type in a sample of 100 individuals?
     Prob(none in 100) = 0.99¹⁰⁰ = 0.366

   • How many individuals do we need to sample to have a 90 percent probability of seeing AT LEAST one individual with this blood type?
     Prob(at least one in x = 0.9) means Prob(none in x) = 0.10 or .99^x = 0.10

     log(.99^x ) = log(0.10) or x* log(.99 ) = log(0.10) or

     x = log(0.10) / log(.99 ) = 229