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An unbiased circular spinner has a movable pointer and five equal sectors, two coloured green and three coloured red - Leaving Cert Mathematics - Question a - 2013
Question a
An unbiased circular spinner has a movable pointer and five equal sectors, two coloured green and three coloured red. (i) Find the probability that the pointer stop... show full transcript
Worked Solution & Example Answer:An unbiased circular spinner has a movable pointer and five equal sectors, two coloured green and three coloured red - Leaving Cert Mathematics - Question a - 2013
Step 1
Find the probability that the pointer stops on green for one spin of the spinner.
Answer
To find the probability that the pointer stops on green:
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Determine the total number of sectors: 5
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Count the number of green sectors: 2
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The probability can be calculated using the formula:
Therefore, the probability that the pointer stops on green for one spin of the spinner is (0.4) or (40%).
Step 2
List all the possible outcomes of 3 successive spins of the spinner.
Answer
The possible outcomes of 3 successive spins can be represented as a sequence of letters where 'G' represents green and 'R' represents red. Since each spin has 2 options (Green or Red), the number of outcomes can be calculated as:
The list of all possible outcomes is:
- GGG
- GGR
- GRG
- GRR
- RGG
- RGR
- RRG
- RRR
Step 3
Complete the following table:
Answer
For part (b), the table showing outcomes based on winnings from 3 spins:
| Player wins | €0 | €1 | €2 | €3 |
|---|---|---|---|---|
| Required outcomes | 6 | 3 | 3 | 1 |
- €0: Represents outcomes where no greens appear (RRR).
- €1: Represents outcomes where one green appears (G, R, R combinations).
- €2: Represents outcomes where two greens appear (G, G, R combinations).
- €3: Represents outcomes where three greens appear (GGG).
Step 4
Is one spin of the spinner above an example of a Bernoulli trial?
Answer
Yes, one spin of the spinner is an example of a Bernoulli trial. A Bernoulli trial is defined as a random experiment where there are only two possible outcomes. In this case, a spin can result in either green (success) or red (failure), fulfilling the criteria for a Bernoulli trial.