Chapter 3. Probability

72 Chapter 3: Probability3. X-Linked DisorderWhen none of 12 males have a particular X-linked recessive gene, the probability of not having the gene is1.000, thus the probability of at least one having the gene would be 1 minus the probability of not having thegene, or 1 – 0= 1.000.4. Type O bloodWhen five different blood samples include at least one with type O blood, a probability of 0.20, the probabilityof having five samples that do not include at least one (i.e. none) with type O blood is 1 minus the probability ofhaving a sample with at least one with type O blood, or 1 minus 0.20 or 0.80.5. Subjective Conditional ProbabilityIt would be very unusual that the same credit card would be used in several different countries on the same day,assuming the person had to use it in person and the countries were not close to each other. Therefore, it is likelythat it was being fraudulently used, thus the subjective conditional probability is close to 1.6. Subjective Conditional ProbabilityWe estimate the probabilities in this case. From our daily observation it seems that males use or ownmotorcycles more than females. Let’s estimate the conditional probability of selecting a male given that theperson owns a motorcycle at about 0.95. A criminal investigator who finds out a motorcycle is registered to PatRyan, it would be reasonable to assume that Pat Ryan is a male.7. Probability of At Least One Girl out of five childrenFind probability of the complement of A where A is a girl:P( A )= P(boy and boy and boy and boy and boy)= 0.5 5 = 0.0313P(of at least one girl)= 1.0000 – P( A )=1.0000 – 0.0313= 0.9687The parents should be pretty confident that out of five children, at least one of them would be a girl.8. Probability of At Least One Girl out of twelve childrenFind probability of the complement of A where A is a girl:P( A )= P(boy and boy ....and.... boy and boy and boy)= 0.5 12 = 0.000244P(of at least one girl)= 1.000000 – P( A )=1.000000 – 0.000244= 0.999756If the parents have twelve children and none are girls, the probability of this happening by chance is 0.000244or about 2 times out of 10,000. The parents can conclude that this is a very rare outcome.9. Probability of a Girl as third child after two boysThese are independent events so the probability of getting a girl as the third child is 0.5 and there is no influenceon that probability from the sex of the first two children.No, the probability of getting three girls out of three children would be:P(three girls)= (girl and girl and girl)= 0.5 3 = 0.125This is not the same probability as getting a girl as the third child after having two boys.10. Mendelian GeneticsP(green pod and purple flower)=P(green pod)514 0.3571= =8 0.571414P(purple flower | green pod)= 0. 62511. Clinical Trials of Pregnancy Test11P(not pregnant and negative test) 99 0.1111= = =P(not pregnant) 14 0.141499P(negative test | not pregnant)= 0. 786She should probably be somewhat concerned that the test may not have accurately described the situation.There is a 0.786 probability that she will get a negative test when she is not pregnant.