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Li throws two fair four-sided dice, each numbered 1, 2, 3 and 4 - OCR - GCSE Maths - Question 18 - 2021 - Paper 1
Question 18
Li throws two fair four-sided dice, each numbered 1, 2, 3 and 4. Li multiplies together the two numbers that the dice land on to produce a score. Find the probabili... show full transcript
Worked Solution & Example Answer:Li throws two fair four-sided dice, each numbered 1, 2, 3 and 4 - OCR - GCSE Maths - Question 18 - 2021 - Paper 1
Step 1
Identify Possible Outcomes
Answer
When Li throws two four-sided dice, the potential outcomes can be calculated by multiplying each face of the first die by each face of the second die. Thus, the total outcomes are as follows:
- Possible scores: 1, 2, 3, 4 (from die 1)
- Possible scores: 1, 2, 3, 4 (from die 2)
The possible products of these outcomes (for both dice) yield:
- 1 x 1 = 1
- 1 x 2 = 2
- 1 x 3 = 3
- 1 x 4 = 4
- 2 x 1 = 2
- 2 x 2 = 4
- 2 x 3 = 6
- 2 x 4 = 8
- 3 x 1 = 3
- 3 x 2 = 6
- 3 x 3 = 9
- 3 x 4 = 12
- 4 x 1 = 4
- 4 x 2 = 8
- 4 x 3 = 12
- 4 x 4 = 16
Thus the complete list of scores is: 1, 2, 3, 4, 4, 6, 8, 3, 6, 9, 12, 4, 8, 12, 16.
Step 2
Determine Prime Numbers
Answer
A prime number is defined as a natural number greater than 1 that has no positive divisors other than 1 and itself. From the computed scores, we identify the prime numbers:
- Prime numbers found: 2, 3
Note that 1 is not a prime number, and other products such as 4, 6, 8, 9, 12, 16 are not prime.
Step 3
Step 4