a) Show that if A is a fixed event of positive probability, then the function Q [B]=P[B|A] taking events B into IR satisfies the three defining axioms of probability. b) 16. A credit card company studies past information on its cardholders. It determines that an index of riskiness on a scale from 1 to 5, based on factors such as number of charge accounts, total amount owed, family income, and others, might help identify new card applicants who will later default on their debts. They find that among their past defaulters, the distribution of index values was: 1:2%, 2: 15%, 3: 22%, 4: 28%, 5: 33%. Among non-defaulters the distribution of index values was: 1:28%, 2: 25%, 3: 18%, 4: 16%, 5: 13%. It is known that about 5% of all card holders default. What is the probability that a new card applicant with an index of 5 will default? Repeat the computation for the other index values 4 through 1.