too many gumballs

[hilarysears77]

i am pulling my hair out over this chapter on probability.
First question which formula do I use to determine this answer.

A gumball machine contains 300 grape flavored balls, 400 cherry flavored balls, and 500 lemon flavored balls. What is the probability of getting 1 grape ball, 1 cherry ball, and 1 lemon ball if each ball was removed and then replaced before choosing the next from the machine?
a) 0.0264
b) 0.0531
c) 0.0347
d) 0.0482
i got answer c
but i have no clue how the heck i got to that answer.
p.s i just started learning statisitcs, any info or tools of the trade will be greatly appreciated
please help :confused:
utterly confused
hilary

[JohnM]

Hilary,

There are a total of 1200 gumballs.

If you pick out 1 gumball, the probability of it being grape is the number of grape gumballs divided by total number of all gumballs, so it is

=300/1200 = 1/4 or 0.25

Same principle for cherry and lemon:

cherry = 400/1200 = 1/3 or 0.333

lemon = 500/1200 = 5/12 or 0.4167

Now, in order to pick one of each flavor (assuming it is replaced), you are essentially picking 1 grape AND 1 cherry AND 1 lemon.

Multiply the individual probabilities together, since they are independent* of each other:

P = 0.25 * 0.333 * 0.4167

= 0.0347

*independent means that since you replace each gumball after picking it, that selection has no effect on the probability of any other selection