Question

A hat contains twenty green slips of paper numbered 1 through 20, ten white slips of paper numbered 1 through 10, forty yellow slips of paper numbered 1 through 40, and 10 blue slips of paper numbered 1 through 10. If these 80 slips of paper are thoroughly shuffled so that each slip has the same probability of being drawn, find the probability of drawing a slip of paper that is:________

1) Blue or green
2) Numbered 1, 2, 3, 4, or 5
3) White or yellow and numbered 1, 2, 3, or 4
4) Numbered 5, 15, 25, or 35
5) Green and numbered higher than 12 or yellow and numbered higher than 26

Answer 1

1)
`(3)/(8)`

2)
`(1)/(4)`

3)
`(1)/(10)`

4)
`(1)/(10)`

5)
`(11)/(40)`

Explanation:

Let's denote each colour by its first letter i.e. B = Blue, G = Green, W = White, Y = Yellow.

B = 10

G = 20

W = 10

Y = 40

1) P(B or G) =
`(10+20)/(80)=(3)/(8)`

2) Each of the four colours has the numbers 1 to 5.

P(1,2,3,4,5) =
`(4*5)/(80)=(1)/(4)`

3) Each of yellow and blue has the numbers 1, 2, 3 and 4.

P((W or Y) and (1,2,3,4) ) =
`(4*2)/(80)=(1)/(10)`

4) 5 appears in the 4 colours, 15 appears in G and Y, 25 and 35 appear in Y only.

P(5,15,25,35) =
`(4+2+1+1)/(80)=(1)/(10)`

5) There are 8 numbers higher than 12 in G and 14 numbers higher than 26 in Y.

P((G and >12) or (Y and >26)) =
`(8+14)/(80)=(11)/(40)`