Probability when using a spinner twice

Question

Derek and Clarissa are playing a game using a spinner with five evenly sized sections labeled 1 – 5. Each player spins the spinner twice and records the sum of the two numbers. Derek wins if the sum is even. Clarissa wins if the sum is odd.

Who has the greater chance of winning?

Answer 1

When starting such probability questions, it's a good idea to begin with stating the sample space: that is, all possible outcomes. Then, we can narrow down to the probability of particular events; in this case, the event of an even sum and the event of an odd sum. The probability for an event will be the number of ways the event can happen divided by total sample space.

Sample Space

Each outcome consists of two spins. This can include repeat numbers. Since each spin has 5 possible numbers with an equal chance of happening, and we have two spins, our sample space is:

5 x 5 = 25

Now we know that the denominator for our probability calculations will be 25.

Event Space

Let's make a table with all the outcome pairs, their sums, and corresponding event (even or odd)

Spin 1 Spin 2 Sum Event

1 1 2 Even

1 2 3 Odd

1 3 4 Even

1 4 5 Odd

1 5 6 Even

2 1 3 Odd

2 2 4 Even

and so on...

The total number of ways the event can happen will be the numerator for our probability.

The number of even events is 13. The spin pairs are: [1, 1], [1, 3], [1, 5], [2, 2], [2, 4], [3, 1], [3, 3], [3, 5], [4, 2], [4, 4], [5, 1], [5, 3], [5, 5].

Using the number above and the denominator we got from the sample space, the probability of an even event is: 13/25

The number of odd events is 12. The spin pairs are: [1, 2], [1, 4], [2, 1], [2, 3], [2, 5], [3, 2], [3, 4], [4, 1], [4, 3], [4, 5], [5, 2], [5, 4].

Using the number above and the denominator we got from the sample space, the probability of an odd event is: 12/25

Final Answer

Since the probability of an even event (13/25) is greater than that of an odd event (12/25), Derek has a greater chance of winning.