Question

In: Statistics and Probability

The following two-way contingency table gives the breakdown of the population of adults in a particular...

The following two-way contingency table gives the breakdown of the population of adults in a particular locale according to employment type and level of life insurance:

	Level of Insurance
Employment Type	Low	Medium	High
Unskilled	0.07	0.19	0.00
Semi-skilled	0.04	0.28	0.08
Skilled	0.03	0.18	0.05
Professional	0.01	0.05	0.02

An adult is selected at random. Find each of the following probabilities.
a. The person has a high level of life insurance.
b. The person has a high level of life insurance, given that he does not have a professional position.
c. The person has a high level of life insurance, given that he has a professional position.
d. Determine whether or not the events “has a high level of life insurance” and “has a professional position” are independent.

Expert Solution

Solution :

Probability of an event E is given by,

a) P(high) = (0.00 + 0.08 + 0.05 + 0.02)

P(high) = 0.15

Hence, the probability that a randomly selected adult has a high level of insurance is 0.15.

b) We have to find P(high | not professional)

Hence, the probability that The person has a high level of life insurance, given that he does not have a professional position is 0.1413.

c) We have to find P(high | professional)

Hence, the probability that The person has a high level of life insurance, given that he has a professional position is 0.25.

d) Two events "“has a high level of life insurance” and “has a professional position" are said to be independent iff,

P(high and professional) = P(high).P(professional)

We have,

P(high and professional) = 0.02

P(high) = 0.15

P(professional) = 0.05

P(high).P(professional) = (0.15 × 0.05) = 0.0075

Hence, the events has a high level of life insurance” and “has a professional position” are not independent.

orchestra answered 2 years ago

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