Question

People from East Coast and Midwest carry different types of credit cards. Credit Card Visa Master American Express Discover East Coast 0.45 0.37 0.16 0.02 Midwest 0.40 0.43 0.03 ? (a) What is the probability that a person from Midwest has Discover card? (b) What is the probability that a person chosen at random from East Coast and Midwest, independently of one another, both have type American Express? (c) What is the probability that a person chosen at random from East Coast and Midwest, independently of one another, both have the same type of credit ca

Answer 1

A. 0.14

B. 0.0048

C. 0.3467

Explanation:

You are given the table

`\begin{array}{ccccc}\text{Credit Card}&\text{Visa}&\text{Master}&\text{American Express}&\text{Discover}\\ \\\text{East Coast}&0.45&0.37&0.16&0.02\\\text{Midwest}&0.40&0.43&0.03&?\end{array}`

The sum in each row must be equal to 1, so

`0.40+0.43+0.03+?=1\\ \\?=1-0.86=0.14`

Hence, the table is

`\begin{array}{ccccc}\text{Credit Card}&\text{Visa}&\text{Master}&\text{American}&\text{Express}\\ \\\text{East Coast}&0.45&0.37&0.16&0.02\\\text{Midwest}&0.40&0.43&0.03&0.14\end{array}`

A. The probability that a person from Midwest has Discover card is

`0.14`

B. The probability that a person chosen at random from East Coast and Midwest, independently of one another, both have type American Express is

`0.16\cdot 0.03=0.0048`

C. The probability that a person chosen at random from East Coast and Midwest, independently of one another, both have the same type of credit card is

`0.45\cdot 0.40+0.37\cdot 0.43+0.16\cdot 0.03+0.02\cdot 0.14=0.3467`