According to a survey, the probability that a family owns two cars if their annual income is greater than rs. 8 lakh is 0.75. of the households surveyed, 60 per cent had income over rs. 8 lakh and 52 per cent had two cars. what is the probability that a family has two cars and an income over rs. 8 lakh a year?
Answers
P(annual income is greater than 8 lakhs) = 0.60
P(2 cars) = 0.52
P(owns 2 cars and annual income is greater than 8 lakhs) = 0.75 x 0.60 = 0.45
Given,
If a family's annual income exceeds Rs. 8 lakh, the probability that they possess two automobiles is 0.75.
The probability of earning more than Rs. 8 lakh in a year is 0.60.
The probability that the household has two automobiles is 0.52.
To find,
The probability that a household owns two automobiles and earns more than Rs. 8 lakh per year.
Solution,
The probability that a household owns two automobiles and earns more than Rs. 8 lakh per year is 0.45.
We can easily answer this numerical problem using the approach outlined below.
We know that,
P(two cars and income greater than Rs. 8 lakh) = 0.75
P(income above Rs. 8 lakh) = 0.60
P(two cars) = 0.52
Now,
P(two cars and income above Rs. 8 lakh) = 0.60 x 0.75
= 0.45
As a result, the probability that a household owns two automobiles and earns more than Rs. 8 lakh per year is 0.45.