Question

5. Through a telephone survey, a low-interest bank credit card is offered to 100 as follows. Income $50,000 Income> $50,000 40 30 Accept offer Reject offer 120 210 a. Develop a joint probability table and show the marginal probabilities.. b. What is the probability of a household whose income exceeds $50,000 and who rejects the offer c. If income is <$50,000, what is the probability the offer will be accepted? . If the offer is accepted, what is the probability that income exceeds $50,000?

Answer 1

If we divide every number by 400 then we will get the joint probability table,

a.

	Income <50000	Income > 50000	Marginal Prob
Accept Offer	40/400	30/400	70/400
Reject Offer	210/400	120/400	330/400
Marginal Prob	250/400	150/400

b.

There are total 30 + 120 (column 2) households having income greater than 50000 dollars, out of them 120 reject the offer,

Probability = 120/150 = 0.8

c.

There are total 40 + 210 (column 1) households having income less than 50000 dollars, out of them 40 accepts the offer,

Probability = 40/250 = 0.16

d.

There are toal 40 + 30 (row 1) households which accept the offer,

Out of them, 30 has income more than 50000

Thus, probability = 30/70 = 0.43