a b It is estimated that of all California adults are colle

(a)

(b)

It is estimated that % of all California adults are college graduates and that % of California adults are regular internet users. It is also estimated that % of California adults are both college graduates and regular internet users. (a) Among California adults, what is the probability that a randomly chosen internet user is a college graduate? Round your answer to decimal places. (b) What is the probability that a California adult is an internet user, given that he or she is a college graduate? Round your answer to decimal places. (If necessary, consult a list of formulas.)

Solution

We add probabilities of two events if we want to find out if one event or another could happen. However, if we want to know the probability of both the events happening together, we multiply the probabilities of the two events happening individually.

a) We know that 26 out of every 100 Californian adults are college graduates and 31 out of every 100 Californian adults are internet users. Also, 20 out of every 100 Californian adults are both college graduates and internet users. So, among Californian adults, we are choosing from the 31 internet users. From these 31 people, we want to know the chances of choosing a college graduate. Since 20% of all Californian adults are internet users and college graduates, we multiply that to the 31 % internet users. Thus, the probability of a randomly chosen internet user being a college graduate is .0.31*.0.20=0.062 or 6.20%

b) The probability of a California adult who is a college graduate ( probability 0.26) being an internet user also ( probability 0.20) is   0.26* 0.20=0.052 or 5.20 %