Expert: Chanda Walker - 3/23/2009

Question
QUESTION: Jane has a bag containing a mix of seeds for purple flowers, yellow flowers and orange flowers in the ratio of 1:1:2, respectively. There is a total of 16 seeds in the bag. Jane randomly sprinkles 3 seeds in a garden. If each of the seeds sprinkled successfully produces 1 flower, what is the probability that there are 2 purple flowers and 1 yellow flower produced? Express your answer as a common fraction.

I know the p(purple) = 4/16, p(yellow)= 4/16, and p(orange)=8/16 since the ratio is 1:1:2.  Correct?  Then, is the probability of 2 purple and 1 yellow (since order does not matter) 4/16 x 3/15 x 4/16 or 1/80?  Thank you for your help.

ANSWER: 16 seeds in the bag so 16 is our denominator.

There are 4 purple, 4 yellow and 8 orange.

Not quite right . . .

(4/16) * (3/15) * (4/12) = (1/4)*(1/5)*(1/3) = 1/60

---------- FOLLOW-UP ----------

QUESTION: Wait...I'm still confused with 4/12. Aren't there 14 seeds still left in the bag?  How did you get that? If you choose the yellow one first, does it change the answer?

Answer
sorry!  My little one got a skinned knee in the middle of working this problem and I totally lost my train of thought.

You're right, just a typo.

(4/16) * (3/15) * (4/14) = (1/4)*(1/5)*(2/7) = 2/140 = 1/70

If you choose the yellow first you get

(4/16)*(4/15)*(3/14) which gives the same answer.

The denominators stay the same, only the numerators move around but that doesn't change the answer.

But there are three ways to get this answer:  bby, byb, ybb so you have to multiply by 3.

3/70