PLEASE HELP

There are 4 green gumballs, 6 red gumballs and 2 yellow gumballs in a gumball machine. If you randomly take two gumballs, what is the probability that you will get two of the same colored gumballs?

The probability that you will get two of the same colored gumballs WITHOUT reposition is 5/15,972 or 0.0003%, and the probability that you will get two of the same colored gumballs WITH reposition is 1/1,296 or 0.0008%

Step-by-step explanation:

Let's recall that the formula of the probability is:

Probability = Number of favorable outcomes/Total number of favorable outcomes

Total number of favorable events = 4 + 6 + 2 = 12

Reposition means that we take the gumball and put it back in the machine.

1. Therefore, the probability of getting two green gumballs without reposition is:

Probability of the 1st gumball to be green = 4/12

Probability of the 2nd gumball to be green = 3/11

Probability of getting two green gumballs without reposition = 4/12 * 3/11 = 12/132 = 3/33 = 1/11

The probability of getting two green gumballs with reposition is:

Probability of the 1st gumball to be green = 4/12

Probability of the 2nd gumball to be green = 4/12

Probability of getting two green gumballs with reposition = 4/12 * 4/12 = 16/144 = 1/9

2. Therefore, the probability of getting two red gumballs without reposition is:

Probability of the 1st gumball to be red = 6/12

Probability of the 2nd gumball to be red = 5/11

Probability of getting two red gumballs without reposition = 6/12 * 5/11 = 30/132 = 5/22

The probability of getting two red gumballs with reposition is:

Probability of the 1st gumball to be red = 6/12

Probability of the 2nd gumball to be red = 6/12

Probability of getting two red gumballs with reposition = 6/12 * 6/12 = 36/144 = 1/4

3. Therefore, the probability of getting two yellow gumballs without reposition is:

Probability of the 1st gumball to be yellow = 2/12

Probability of the 2nd gumball to be yellow = 1/11

Probability of getting two yellow gumballs without reposition = 2/12 * 1/11 = 2/132 = 1/66

The probability of getting two yellow gumballs with reposition is:

Probability of the 1st gumball to be yellow = 2/12

Probability of the 2nd gumball to be yellow = 2/12

Probability of getting two red gumballs with reposition = 2/12 * 2/12 = 4/144 = 1/36

Finally, the probability that you will get two of the same colored gumballs WITHOUT reposition is:

1/11 * 5/22 * 1/66 = 5/15.972 or 0.0003%

and the probability that you will get two of the same colored gumballs WITH reposition is:

1/9 * 1/4 * 1/36 = 1/1,296 or 0.0008%

the answer is here: : )

:

a

step-by-step explanation:

a