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

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 =
`(number of required outcomes)/(number of possible outcomes)`

=
`(300)/(1200)*(400)/(1200)*(500)/(1200)   +(300)/(1200)*(500)/(1200)*(400)/(1200)   +(400)/(1200)*(300)/(1200)*(500)/(1200)  \\ \\+(400)/(1200)*(500)/(1200)*(300)/(1200)   +(500)/(1200)*(300)/(1200)*(400)/(1200)   +(500)/(1200)*(400)/(1200)*(300)/(1200)`

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

=0.20832