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Jack rolls a fair die and spins a fair spinner as shown - Junior Cycle Mathematics - Question 8 - 2012
Question 8
Jack rolls a fair die and spins a fair spinner as shown. (a) Complete the table below showing all possible outcomes. Die Spinner |... show full transcript
Worked Solution & Example Answer:Jack rolls a fair die and spins a fair spinner as shown - Junior Cycle Mathematics - Question 8 - 2012
Step 1
Complete the table below showing all possible outcomes.
Answer
To complete the table, we need to fill in all combinations of the outcomes from rolling a die (1 through 6) and spinning the spinner (A, B, C, D). Thus, the completed table is:
| A | B | C | D | |
|---|---|---|---|---|
| 1 | (1,A) | (1,B) | (1,C) | (1,D) |
| 2 | (2,A) | (2,B) | (2,C) | (2,D) |
| 3 | (3,A) | (3,B) | (3,C) | (3,D) |
| 4 | (4,A) | (4,B) | (4,C) | (4,D) |
| 5 | (5,A) | (5,B) | (5,C) | (5,D) |
| 6 | (6,A) | (6,B) | (6,C) | (6,D) |
Step 2
How many possible outcomes are there?
Answer
The total number of possible outcomes can be calculated by multiplying the number of outcomes from the die (6 possible outcomes) by the number of outcomes from the spinner (4 possible outcomes). Therefore,
Total outcomes = 6 (die) × 4 (spinner) = 24 possible outcomes.
Step 3
Step 4
What is the probability that an outcome will contain an even number?
Answer
The even numbers from rolling a die are 2, 4, and 6, which give us the following outcomes:
- (2,A), (2,B), (2,C), (2,D)
- (4,A), (4,B), (4,C), (4,D)
- (6,A), (6,B), (6,C), (6,D)
In total, there are 12 outcomes with an even number. Thus, the probability can be calculated as:
Probability = ( \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{12}{24} = \frac{1}{2} )