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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

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Answer

When throwing two four-sided dice, each die has 4 faces. Therefore, the total number of possible outcomes is:

$4 imes 4 = 16$

The possible outcomes (score) when multiplying the results from both dice are:
1, 2, 3, 4, 1, 2, 3, 4

Calculating each combination:

(1,1) = 1
(1,2) = 2
(1,3) = 3
(1,4) = 4
(2,1) = 2
(2,2) = 4
(2,3) = 6
(2,4) = 8
(3,1) = 3
(3,2) = 6
(3,3) = 9
(3,4) = 12
(4,1) = 4
(4,2) = 8
(4,3) = 12
(4,4) = 16

Step 2

Identify Prime Numbers

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Answer

From the possible scores, we identify the prime numbers. The prime numbers from our outcomes are:

Therefore, the prime scores are: 2 and 3.

Step 3

Calculate Probability

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Answer

The number of successful outcomes (prime scores) is 2 (i.e., 2 and 3).
Thus, the probability is given by:

$P = \frac{\text{Number of prime scores}}{\text{Total outcomes}} = \frac{2}{16} = \frac{1}{8}$

Thus, the probability that Li's score is a prime number is (\frac{1}{8}).

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