Question

Hartley has two 4-section spinners, each labeled 1-4. She will spin both spinners a total of 96 times. For each pair of numbers where the pointers of the spinners land on, Hartley will subtract the smaller number from the greater number.

How many possible total outcomes are there?

How many times should Hartley spin a difference of 1?

How many times should Hartley spin a difference of 0?

Answer 1

1) Total outcomes of 1 time = 16

2) 36 times

3) 24 times

Explanation:

1) Total outcomes

If both spinners are spinning together, and are labelled from 1 to 4, the the outcome are:

{(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (3, 4), (4, 1), (4, 2), (4, 3), (4, 4)}

We can count them to find total no. of outcomes

Total outcomes = 16

2) When Difference = 1

Following combinations have a difference of 1

{(1, 2), (2, 1), (2, 3), (3, 2), (3, 4), (4, 3)}

n = 6

Probability of getting such combination is: 6/16

How many times Harvey would get such a combination out of 96 times?

`(6)/(16)\cdot96=36`

3) When Difference = 0

Following combinations have a difference of 0

{(1, 1), (2, 2), (3, 3), (4, 4)}

n=4

Probability of getting such combination is: 4/16

How many times Harvey would get such a combination out of 96 times?

`(4)/(16)\cdot96=24`