Question

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?

Answer 1

Answer:

Pr(of getting 1grape ball, 1 cherry ball and 1 lemon ball) =0.20832

Step-by-step explanation:

Let the grape falvored ball be represented by G,

            Cherry flavored balls be C

            Lemon flavored balls be L

the possible order of picks for getting 1grape ball, 1 cherry ball and 1lemon ball are;  GCL or GLC or CGL or CLG or LGC or LCG

Pr(of getting 1grape ball, 1 cherry ball and 1 lemon ball)

  = Pr(GCL) or Pr(GLC) or Pr(CGL) or Pr(CLG) or Pr(LGC) or Pr(LCG)

with replacement we have;

Probability = $\frac{number of required outcomes}{number of possible outcomes}$

=  $\frac{300}{1200}*\frac{400}{1200}*\frac{500}{1200} +\frac{300}{1200}*\frac{500}{1200}*\frac{400}{1200} +\frac{400}{1200}*\frac{300}{1200}*\frac{500}{1200} \\ \\+\frac{400}{1200}*\frac{500}{1200}*\frac{300}{1200} +\frac{500}{1200}*\frac{300}{1200}*\frac{400}{1200} +\frac{500}{1200}*\frac{400}{1200}*\frac{300}{1200}$

= 0.03472 + 0.03472 +0.03472 + 0.03472 + 0.03472 + 0.03472

=0.20832