Question

Suppose we spin the following spinner with the first spin giving the numerator and the second spin giving the denominator of a fraction. What is the probability that the fraction will be less than or equal to 3/2?

Answer 1

EXPLANATION

The probability that the fraction will be less than or equal to 3/2 is given by the following relationship:

`\text{Probability(event)}=\frac{Number\text{ of favourable outcomes}}{\text{Total number of possible outcomes}}`

Now, we can list all the possible fractions that we could get:

Here are the combinations with 4 as the numerator:

4 / 4

4 / 6

4 / 5

4 / 3

Here are the combinations with 6 as the numerator:

6/ 4

6 / 6

6 / 5

6 / 3

Here are the combinations with 5 as the numerator:

5/ 4

5 / 6

5 / 5

5 / 3

Here are the combinations with 3 as the numerator:

3/ 4

3 / 6

3 / 5

3 / 3

As we can see, the are 4*4= 16 different combinations that we could get.

Now, we need to define wich possible combinations are less or equal than 3/2=1.5.

4 / 4 = 1 [LESS THAN 3/2]

4 / 6 = 2/3 = 0.67 [LESS THAN 3/2]

4 / 5 = 0.8 [LESS THAN 3/2]

4 / 3 = [LESS THAN 3/2]

-------------

6/ 4 = 3/2 [EQUAL THAN 3/2]

6 / 6 = 1 [LESS THAN 3/2]

6 / 5 = [LESS THAN 3/2]

6 / 3 [NO --> GREATER THAN 3/2]

------------

5/ 4 = 1.25 [LESS THAN 3/2]

5 / 6 [LESS THAN 3/2]

5 / 5 [LESS THAN 3/2]

5 / 3 [NO -->GREATER THAN 3/2]

------------

3/ 4 [LESS THAN 3/2]

3 / 6 [LESS THAN 3/2]

3 / 5 [LESS THAN 3/2]

3 / 3 [LESS THAN 3/2]

As we can see, there are 14 possible combinations that are less or equal to 3/2.

Hence,

`P(\text{fraction }\leq3/2)=\frac{\text{ the numbers of fractions less or equal than 3/2}}{\text{ all the possible fractions listed }}=(14)/(16)`

Simplifying:

`P(\text{fraction }\leq3/2)=(7)/(8)`

The probability will be 7/8