Answer:
a) 0.27 = 27% probability that a randomly chosen card holder has annual income $20,000 or less.
b) 0.778 = 77.8% probability that (s)he carries a balance
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
In which
P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
P(A) is the probability of A happening.
a) What is the probability that a randomly chosen card holder has annual income $20,000 or less?
20% of 30%(carry no balance).
30% of 70%(carry balance). So
0.27 = 27% 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?
Conditional probability.
Event A: Annual income of $20,000 or less.
Event B: Carries a balance.
0.27 = 27% probability that a randomly chosen card holder has annual income $20,000 or less
This means that
Probability of a income of $20,000 or less and balance.
30% of 70%, so:
The probability is:
0.778 = 77.8% probability that (s)he carries a balance