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A simulation of a spinner with four equal sectors, coloured red, blue, green and yellow, is conducted 1440 times. The spinner is fair, so each colour has an equal probability of being selected.
What is the exact expected number of times the spinner lands on red? Express your answer as a whole number or exact fraction.
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Explanation
Worked solution and answer (click to reveal)
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Worked solution
- The spinner has four equal sectors: red, blue, green, and yellow. Since the spinner is fair, each colour has an equal probability of being selected.
- The probability of landing on any one colour, including red, is 1 divided by the number of sectors. So, P(red) = 1/4.
- The total number of trials conducted is 1440.
- The expected number of times the spinner lands on red is calculated by multiplying the probability of red by the total number of trials.
- Substitute the values: expected red = (1/4) × 1440.
- Perform the multiplication: 1440 ÷ 4 = 360.
- The result is 360, which is a whole number.
- Since the spinner is fair and the number of trials is large, the expected value is exactly 360.
Reference answer: 360
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