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Algebra 2 help?
Two number cubes are rolled to determine how a token moves on a game board. The sides of each number cube are numbered 1, 2, 3, 4, 5 and 6.
There are two options describing how the token will be moved.
Option A: If the product is even, move forward 7 spaces. Otherwise, move backward 5.
Option B: If the product is even, move forward 5 spaces. Otherwise, move backward 4.
Use mathematical expectation to determine which option offers the greater likelihood of moving closer to the finish line on the game board.
Which statement best explains the better option?
The mathematical expectation of Option A is 4. The mathematical expectation of Option B is 2.75. Option A offers a greater likelihood of advancing to the finish line.
The mathematical expectation of Option A is 2.75. The mathematical expectation of Option B is 4. Option A offers a greater likelihood of advancing to the finish line.
The mathematical expectation of Option A is 4. The mathematical expectation of Option B is 2.75. Option B offers a greater likelihood of advancing to the finish line.
The mathematical expectation of Option A is 2.75. The mathematical expectation of Option B is 4. Option B offers a greater likelihood of advancing to the finish line.
1 Answer
- llafferLv 72 years agoFavorite Answer
Option A: If the product is even, move forward 7 spaces, otherwise move back 5.
Option B: If the product is even, move forward 5 spaces, otherwise move back 4.
The only way for the product of two dice to be odd is if both numbers rolled are odd.
There is a 1/2 chance for one die to be odd. For both to be odd the probability becomes 1/4.
This means that there is a 3/4 chance the product is even. So now we can find the expected value of each option. The higher the expected value the faster you get to the finish line.
To get the expected value, multiply each option (accounting for backward movement with a negative value) by its probability, then add the results.
Option A:
3/4 * 7 = 21/4
1/4 * -5 = -5/4
Add them together to get:
21/4 - 5/4 = 16/4 = 4
Option B:
3/4 * 5 = 15/4
1/4 * -4 = -4/4
Add:
15/4 - 4/4 = 11/4 or 2.75
So for each roll, you will (on average) move further along with option A than option B.
So the answer from your multiple choice is A.
