Question

You have two spinners each with three sections of equal size labeled with numbers 1,2,3. You spin both and observe the numbers. Let x be the sum of the two numbers. Find the probability distribution for X.

Answer 1

From the given problem with two spinners with three sections of equal size labeled as 1, 2, and 3.

Spinner 1 : 1 2 3

Spinner 2 : 1 2 3

The sum is as follows :

1+1 = 2

1+2 = 3

1+3 = 4

2+1 = 3

2+2 = 4

2+3 = 5

3+1 = 4

3+2 = 5

3+3 = 6

There are 9 total outcomes

There are (1) 2,

(2) 3's

(3) 4's

(2) 5's

and

(1) 6

and their corresponding probability can be calculated by :

$\text{probability}=\frac{\text{ quantity}}{\text{ total quantity}}$

Probability of 2 = 1/9

Probability of 3 = 2/9

Probability of 4 = 3/9 or 1/3

Probability of 5 = 2/9

Probability of 6 = 1/9

Construct the probability distribution :

To check if your probability distribution is correct.

The sum of P(X) must be equal to 1

1/9 + 2/9 + 1/3 + 2/9 + 1/9 = 1

Therefore the distribution is correct.