Question

A game is played by spinning a wheel that is divided into four sectors, each with a different point value. The angle made at the centre of the circle for each section, and the corresponding point value for each sector is shown in the chart below: Central Angle Point 144° 108° 72° 36° point value 20 30 40 50

Answer 1

What is the expected value of the points earned if the wheel is spun once?

To find the expected value, we need to multiply each point value by its corresponding probability and then add up these products. The probability of landing on each sector can be found by dividing the central angle of that sector by the total central angle of the circle, which is 360 degrees. So we have:

Probability of landing on 20 points: 144°/360° = 0.4

Probability of landing on 30 points: 108°/360° = 0.3

Probability of landing on 40 points: 72°/360° = 0.2

Probability of landing on 50 points: 36°/360° = 0.1

Now we can calculate the expected value:

Expected value = (20 x 0.4) + (30 x 0.3) + (40 x 0.2) + (50 x 0.1)

Expected value = 8 + 9 + 8 + 5

Expected value = 30

Therefore, the expected value of the points earned if the wheel is spun once is 30.

Answer 2

30 points

Explanation:

It sounds like you have a game where you spin a wheel that has four sectors with different point values assigned to them. The chart shows the central angle and the corresponding point value for each sector.

To calculate the expected value (average score) for a single spin of the wheel, you need to multiply each point value by the probability of landing in that sector, and then add up the results. The probability of landing in each sector can be calculated by dividing the central angle of the sector by the total central angle of the wheel (which is 360 degrees).

So, let's calculate the expected value:

Sector 1: Central angle = 144°, Point value = 20

Probability = 144° / 360° = 0.4

Contribution to expected value = 0.4 * 20 = 8

Sector 2: Central angle = 108°, Point value = 30

Probability = 108° / 360° = 0.3

Contribution to expected value = 0.3 * 30 = 9

Sector 3: Central angle = 72°, Point value = 40

Probability = 72° / 360° = 0.2

Contribution to expected value = 0.2 * 40 = 8

Sector 4: Central angle = 36°, Point value = 50

Probability = 36° / 360° = 0.1

Contribution to expected value = 0.1 * 50 = 5

Total expected value = 8 + 9 + 8 + 5 = 30

Therefore, the expected value for a single spin of the wheel is 30 points