Algebra 2 help!

Question

A hat contains 5 balls. The balls are numbered 2, 3, 4, 6, and 8. One ball is randomly selected

and not replaced, and then a second ball is selected. The numbers on the 2 balls are added

together

A fair decision is to be made about which one of two routes to take on a road trip, using the sum

of the numbers on the balls.

The road trip options are the highway or the back roads.

Which description accurately explains how a fair decision can be made in this situation?

If the sum of the balls is less than 10, take the highway. If the sum of the balls is 10 or more, take the back roads.

If the sum of the balls is even, take the highway. If the sum of the balls is odd, take the back roads.

If the sum of the balls is a multiple of 3, take the highway. If the sum of the balls is not a multiple of 3, take the back roads.

If the sum of the balls is a prime number, take the highway. If the sum of the balls is not a prime number, take the back roads.

Answer 1

Using the following table...

2 3 4 6 8

=====================

2 | X 5 6 8 10

3 | 5 X 7 9 11

4 | 6 7 X 10 12

6 | 8 9 10 X 14

8 | 10 11 12 14 X

20 possible outcomes...

X means it cannot happen

Option #1:

Prob(highway) = Prob(sum <10) = 10/20 = 1/2

Prob(back roads) = Prob(sum>=10) = 10/20 = 1/2

Option #2:

Prob(highway) = Prob(even) = 12/20 = 3/5 = 0.6

Prob(back roads) = Prob(odd) = 8/20 = 2/5 = 0.4

Option #3:

Prob(highway) = Prob(multiple of 3) = 6/20 = 3/10 = 0.3

Prob(back roads) = Prob(not multiple of 3) = 14/20 = 7/10 = 0.7

OPtion #4:

Prob(highway) = Prob(prime) = 6/20 = 3/10 = 0.3

Prob(back roads) = prob(not prime) = 14/20 = 7/10 = 0.7

First option is most fair

Answer 2

Hello Mallory,

A fair decision means that each road should have a 50% or 1/2 chance of happening so they both have the same chance of being chosen.

So you want to figure out which of the four descriptions has a probability of 1/2 for both parts.

First, you need to list a sample space of all the possibilities so you can find the probability of any result that they give you (such as the sum is less than 10).

You could make a chart with 5 rows and 5 columns, but remember that the same number cannot be picked twice.

2 3 4 6 8

2

3

4

6

8

Then inside the chart, put the sums since they tell you to add the two numbers on the balls. I will start the chart. See if you can complete it. (X means that result is impossible.)

2 3 4 6 8

2 X 5 6 8 10

3 X

4 X

6 X

8 X

You will end of with 20 numbers inside your chart so all probabilities will be out of 20. For the first choice, you would see how many choices inside the table are less than 10. The probability is that number over 20. Do the same for each result, that they give you. You are looking for the choice where the probability for each road is 10/20 because that would make it fair. In the wrong choices one of the probabilities will be higher than the other. See if you can work through the rest of the problem. If you get stuck or want your answer checked, please send in your work.