8. Thirty percent of credit card holders carry no monthly balance, while 70% do. Of those card holders carrying a balance, 30% have annual income $20,000 or less, 40% between $20,001 and $50,000, and 30% over $50,000. Of those card holders carrying no balance, 20%, 30%, and 50% have annual incomes in these three respective categories.

(a) What is the probability that a randomly chosen card holder has annual income $20,000 or less?

(b) If this card holder has an annual income that is $20,000 or less, what is the probability that (s)he carries a balance?

10. The system of components shown in Figure 2-15 below functions as long as components 1 and 2 both function or components 3 and 4 both function. Each of the four components functions with probability 0.9 independently of the others. Find the probability that the system functions.

Figure 2- I 5 System of four components. I I. Find the reliability of a 3outof4 system if each of its four components functions with probability 0.9 indepen dently of the others