Question

Your friend just filled her gumball machine with 100 pieces of gum. She has red, blue, green, orange and purple gumballs in it. The table shows the number of each color she put in. You want to buy two pieces of gum. What is the probability that both gumballs are purple?

15 red
24 purple
30 blue
13 green
18 orange

Answer 1

P(p)=number of purple gumballs divided by total number of gumballs

P(p and p)=P(p)*P(p)  so this is without replacement so we get:

P(pp)=(24/100)(23/99)=552/9900

P(pp)=46/825   (≈5.58%)

Answer 2

So at first there is 24/100, then if you get a purple that brings it to 23/99. Just multiply 24 by 23 and 100 by 99 then simplify that fraction. The answer would be 552/9900 which simplifies to 46/825.