Question

Q.2. The Insurance Regulatory Authority regularly conducts surveys on the coverage of insurance. Latest survey indicates that 30% of population has medical insurance. Suppose a random sample of 3 persons is selected
(a) Draw a neat and complete probability tree for this problem. Show all possible outcomes and their probabilities.
(b) What is the probability that only one person has medical insurance coverage? Show all calculations.
(c) What is the probability that exactly two persons have medical insurance coverage? Show all calculations.

Answer 1

Answer:

Step-by-step explanation:

Draw a neat and complete probability tree for this problem. Show all possible outcomes and their probabilities

Answer 2

The answers are 0.441 and 0.189.

Given:

30% of the population has medical insurance
A sample of 3 persons is selected

To Find:

What is the probability that only one person has medical insurance coverage?

What is the probability that only one person has medical insurance coverage?

Solution:

The probability of a person having medical insurance is 0.3.

Hence the probability of a person not having medical insurance is 0.7.

For only one person to have medical insurance, the probability is

$0.3*0.7*0.7=0.147$ . There are three such cases as there are 3 persons.

Hence the probability of only one person having medical insurance is

$3*0.147=0.441$

For only two persons to have medical insurance, the probability is

$0.3*0.3*0.7=0.063$ . There are three such cases as there are 3 persons.

Hence the probability of only one person having medical insurance is

$3*0.063=0.189$

The probability of only one person having insurance is 0.441 and of only two people having medical insurance is 0.189.

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