Question

A joint survey by Parade magazine and Yahoo! found that 59% of American workers say that if they could do it all over again, they would choose a different career (USA Today, September 24, 2012). The survey also found that 33% of American workers say they plan to retire early and 67% say they plan to wait and retire at age 65 or older. Assume that the following joint probability table applies. Excel File: data04-37.xls a. What is the probability a worker would select the same career (to 2 decimals)? b. What is the probability a worker who would select the same career plans to retire early (to 4 decimals)? c. What is the probability a worker who would select a different career plans to retire early (to 4 decimals)?

Answer 1

Concept and reason

The probability of the event E is denoted as $P(E)$.

The probability that an event will occur given that some other event has already happened is called conditional probability.

Fundamentals

The conditional probability for any two events is given by,

$P({E_1}|{E_2}) = \frac{{P({E_1} \cap {E_2})}}{{P({E_2})}}\;\;\;\;\;\;\;\;;P({E_2}) > 0$

a.

The contingency table is given as,

Career\Retire	Yes	No	Total
Same Career	0.2	0.21	0.41
Different Career	0.13	0.46	0.59
Total	0.33	0.67	1

Compute the probability that a worker would select the same career.

$P({\rm{Same Career)}} = 0.41$ (From the given contingency table)

Therefore, the probability that a worker would select the same career is 0.41.

b.

The contingency table is given as,

Career\Retire	Yes	No	Total
Same Career	0.2	0.21	0.41
Different Career	0.13	0.46	0.59
Total	0.33	0.67	1

Compute the probability that a worker who would select the same career plans to retire early.

Therefore, the probability that a worker who would select the same career plans to retire early is 0.4878.

c.

The contingency table is given as,

Career\Retire	Yes	No	Total
Same Career	0.2	0.21	0.41
Different Career	0.13	0.46	0.59
Total	0.33	0.67	1

Compute the probability that a worker who would select the different career plans to retire early.

Therefore, the probability that a worker who would select the different career plans to retire early is 0.2203.

Ans: Part a

The probability that a worker would select the same career is 0.41.

Part b

The probability that a worker who would select the same career plans to retire early is 0.4878.

Part c

The probability that a worker who would select the different career plans to retire early is 0.2203.