There are red, blue, and black ball pens in a jar. There are 6 red ball pens. The probability of getting a red ball pen is 22.22% while the probability of getting a black ball pen is 40.74%.

Question

a. How many ball pens are there in the jar?

b. How many are black pens in the jar?

c. How many are blue pens in the jar?

Answer 1

P(red pen) = number of red pens/total number of pens

2/9 = 6 / total number of pens

total number of pens is 27

P(black pen) = number of black pens/total number of pens

0.4074 = number of black pens/27

number of black pens = 10.9998 ~ 11

number of blue pens = 27 - number of red pens - number of black pens = 27 - 6 - 11 = 10

Answer 2

a)

P(red) = # red/ total # of pens

We know P(red) = 0.2222 and we know the # red pens = 6. Rearranging the above equation we solve for the total # of pens:

total # of pens = # red/P(red)

= 27.00270027

= 27 pens

The decimals are due to rounding error and we know the total # of pens is therefore 27

= 6 / 0.2222

b)

P(black) = 0.4074

We also know

P(black) = # black/total # of pens

Rearranging this equation we get

# black = P(black)*total # of pens

= 0.4074 * 27

= 10.9998

= 11 black pens

c)

From the previous two problems we know that we have 27 pens and 11 of them are black. We were given that 6 are red. Since there are only black, red and blue balls in the jar we conclude that there are

6 + 11 + # blue pens = 27

# blue pens = 27 - 17

= 10 blue pens