A contractor is required by a country planning department to

A contractor is required by a country planning department to submit one, two, three, four, five, or six forms (depending on the nature of the project) in applying for a building permit. Let Y= the number of forms required of the next applicant. The probability that y forms are required is known to be proportional to y²

Solution

The probability of the number of forms required can be tabulated as below:

The summation of all the probability options should be equal to 1.

i.e k+4k+9k+16k+25k+36k = 1

k=1/91

b) P(atleast two forms selected) = P(2) + P(3)+ P(4) + P(5) + P(6)

= 1 - P(1)

= 1 - k

= 1 - 1/91

= 90/91

c) P(between 3 and 5 forms selected) = P(3) + P(4) + P(5)

= 9k + 16k + 25k

= 50/91