I’ll be posting some of my Math316 subject problems here and of course with its answer, since, I’m taking it up this semester! 😀
Problem # 1:
Two refills of ballpoint are to be selected at random from a box that contains 4 blue, 3 red and 2 black refills. If x is the number of blue and y is number of red refills selected, find:
- The joint probability distribution of x and y.
- P[(x,y)], where A is the region f(x+y) / x+y <=1.
Solution:
a.) The joint probability distribution of x&y.
f(0,0) = 4C0 . 3C0 . 2C2 / 9C2
= 1/36
f(0,1) = 4C0 . 3C1 . 2C1 / 9C2
= 1/6
f(1,0) = 4C1 . 3C0 . 2C1 / 9C2
= 2/9
f(1,1) = 4C1 . 3C1 . 2C0 / 9C2
= 1/3
f(2,0) = 4C2 . 3C0 . 2C0 / 9Cs
= 1/6
f(0,2) = 4C0 . 3C2 . 2C2 / 9C2
= 1/12
b.) P[(x,y)], where A is the region f(x+y) / x+y <=1.
P(A) = p(0,0) + P(0,1) + P(1,0)
= 1/36 + 1/6 + 2/9
= 5/12 (Since, x+y <=1)