GCSE OCR Maths Prime Factors, HCF and LCM: Li throws two fair four-sided di

Li throws two fair four-sided dice, each numbered 1, 2, 3 and 4 - OCR - GCSE Maths - Question 4 - 2021 - Paper 1

Question 4

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 probabilit... 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 4 - 2021 - Paper 1

Step 1

Step 1: Identify the Possible Outcomes

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Answer

When throwing two four-sided dice, the possible outcomes for each die are 1, 2, 3, or 4. The total number of outcomes when rolling two dice is given by:

$4 \times 4 = 16$

This means there are 16 possible scores.

Step 2

Step 2: Calculate the Scores from the Rolls

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Answer

The scores Li could get by multiplying numbers from the two dice are:

(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

Combining equivalent scores gives us: 1, 2, 3, 4, 6, 8, 9, 12, 16.

Step 3

Step 3: Identify Prime Scores

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Answer

A prime number is defined as a number greater than 1 that has no positive divisors other than 1 and itself. From our list, the prime scores are: 2, 3.

Step 4

Step 4: Calculate the Probability

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Answer

The number of favorable outcomes (prime scores) is 2 (2 and 3). Thus, the probability that Li's score is a prime number is given by:

$P(A) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Outcomes}} = \frac{2}{16} = \frac{1}{8}$

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

Li throws two fair four-sided dice, each numbered 1, 2, 3 and 4 - OCR - GCSE Maths - Question 4 - 2021 - Paper 1

Worked Solution & Example Answer:Li throws two fair four-sided dice, each numbered 1, 2, 3 and 4 - OCR - GCSE Maths - Question 4 - 2021 - Paper 1

Step 1: Identify the Possible Outcomes

Step 2: Calculate the Scores from the Rolls

Step 3: Identify Prime Scores

Step 4: Calculate the Probability

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