the problty that an adu have a credit card is .70. 2 adu are selected. the prob. that the first adu. pos a cc?

Question

the probability tht an adult posses a credit card is .70. two adults are selected a random..t he probability that the first adult possess a credi card and the second adult does not posses a credit card is: ??? how do you work this out

Answer 1

If the probability that an adult possesses a credit card is 70%, the probability that the adult does not possess a credit card is 30%. Thus, the probability that an adult either possesses a credit card or does not possess a credit card is 70% + 30%, or 100%.

For your problem, the probability that the first adult possesses a credit card is 70%, and the probability that the second adult does not possess a credit card is 30%. The probability for both to be true and in that order is 70% times 30%, or 21%.

In a more general sense, there are four possible outcomes:
(1) Both adults have credit cards
(2) Only the first adult has a credit card (your problem)
(3) Only the second adult has a credit card
(4) Neither adult has a credit card.

The probability that both adults have credit cards is 70% times 70%, or 49%. Similarly, the probability that neither adult has a credit card is 30% times 30%, or 9%. Since all probabilities must add up to 100%, the probability that only one adult has a credit card is 100% minus 49% for case (1), and minus 9% for case (4). The result is 42% probability that only one adult has a credit card. Realizing that the probability for it to be the first adult is the same as the probability for it to be the second adult, the probability for it to be either one is half of 42%, or 21% as determined above.