Question 4
Complete
5.00 points out
of 8.00
P Flag
question
A banking institution offers three types of credit cards: silver, gold and platinum. Gold and platinum credit cards represent 30% of their customers (each). Considering all customers, 15% have an annual income of $70k, 20% have an annual income of $80k, and 30% receive $90k. Customers with silver cards are equally likely to earn $80k or $100k. Customers with gold cards are equally likely to earn $70k or $90k. Of customers with silver cards, 12.5% and 32.5% have incomes of $70k and $90k, respectively. Of customers making $80k, one-quarter of them have a gold card. Finally, 8/30 of customers with $90k as annual income have a platinum credit card.
1) What proportion of clients have a platinum card and an annual income of $90k?
.08
2) What proportion of clients have a silver or gold card, and an annual income of $80k or $90k?
.39
3) Are having a silver card and an annual income of $100k statistically independent?
not statistically independent
4) From the clients with an annual income of $80k or $100k, what proportion has a gold credit card?
.1613
5) If we select one client, what is the probability that he has a platinum credit card or an annual income of $70k?
.45
6) If we select one client that has a silver credit card, what is the probability that his annual income is at least $90k?
.6
7) What is the percentage of clients with a silver or gold credit card, and an annual income that is not $90k?
.42
8) If we select a client with a platinum credit card, what is the probability that she has an annual income of $70k?
0