Question

PLEASE HELP

Answer 1

Answer:

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%