1. Let $E = \{ \text{even numbers between 1 and 25} \} \newline A = \{ 2, 8, 10, 14 \} \newline B = \{ 6, 8, 20 \} \newline C = \{ 6, 18, 20, 22 \} \newline (a) Complete the Venn diagram for this information. \newline \newline A number is chosen at random from $E$. \newline (b) Find the probability that the number is a member of $A \cap B$.

GCSE Edexcel Maths Scatter Graphs & Correlation: 1. Let $E = \{ \text{even number

1. Let $E = \{ \text{even numbers between 1 and 25} \} \newline A = \{ 2, 8, 10, 14 \} \newline B = \{ 6, 8, 20 \} \newline C = \{ 6, 18, 20, 22 \} \newline (a) Complete the Venn diagram for this information - Edexcel - GCSE Maths - Question 2 - 2018 - Paper 2

Question 2

$1.-Let-$E-=-\{-\text{even-numbers-between-1-and-25}-\}-\newline-A-=-\{-2,-8,-10,-14-\}-\newline-B-=-\{-6,-8,-20-\}-\newline-C-=-\{-6,-18,-20,-22-\}-\newline-(a)-Complete-the-Venn-diagram-for-this-information-Edexcel-GCSE Maths-Question 2-2018-Paper 2.png$

1. Let $E = \{ \text{even numbers between 1 and 25} \} \newline A = \{ 2, 8, 10, 14 \} \newline B = \{ 6, 8, 20 \} \newline C = \{ 6, 18, 20, 22 \} \newline (a) Comp... show full transcript

Worked Solution & Example Answer:1. Let $E = \{ \text{even numbers between 1 and 25} \} \newline A = \{ 2, 8, 10, 14 \} \newline B = \{ 6, 8, 20 \} \newline C = \{ 6, 18, 20, 22 \} \newline (a) Complete the Venn diagram for this information - Edexcel - GCSE Maths - Question 2 - 2018 - Paper 2

Step 1

Complete the Venn diagram for this information.

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Answer

To complete the Venn diagram, we identify the elements in each set and their intersections. \newline \newline - Set A contains the numbers: 2, 8, 10, 14. \newline - Set B contains the numbers: 6, 8, 20. \newline - Set C contains the numbers: 6, 18, 20, 22. \newline \newline The intersections are: \newline - $A \cap B = \{ 8 \}$ . \newline - $B \cap C = \{ 20, 6 \}$ . \newline - $A \cap C = \{ \}$ . \newline - $A \cap B \cap C = \{ \}$ . \newline \newline The complete Venn diagram will show: \newline - Region A contains 2, 10, 14 (Placement in the A circle only). \newline - Region B contains 6 (only), alongside 8 in the overlap with A. \newline - Region C contains 18 and 22 (placement in the C circle only), and 20 in the overlap with B. \newline - The element 8 is thus in the overlap of A and B: \newline - A Venn diagram representation should look as follows: (A) [2, 10, 14], (B) [6], (C) [18, 22], (A ∩ B) [8], (B ∩ C) [20].

Step 2

Find the probability that the number is a member of A ∩ B.

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Answer

The intersection of sets A and B consists of the elements common to both sets. \newline \newline From the previous step, we identified that: \newline - $A \cap B = \{ 8 \}$ . \newline \newline Now, the total number of elements in set $E$ is 12 (all even numbers between 1 and 25: $\{2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24\}$ ). \newline \newline The probability that a number chosen at random from $E$ is a member of $A \cap B$ is calculated as follows: \newline \newline $P(A \cap B) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{1}{12}$

1. Let $E = \{ \text{even numbers between 1 and 25} \} \newline A = \{ 2, 8, 10, 14 \} \newline B = \{ 6, 8, 20 \} \newline C = \{ 6, 18, 20, 22 \} \newline (a) Complete the Venn diagram for this information - Edexcel - GCSE Maths - Question 2 - 2018 - Paper 2

Worked Solution & Example Answer:1. Let $E = \{ \text{even numbers between 1 and 25} \} \newline A = \{ 2, 8, 10, 14 \} \newline B = \{ 6, 8, 20 \} \newline C = \{ 6, 18, 20, 22 \} \newline (a) Complete the Venn diagram for this information - Edexcel - GCSE Maths - Question 2 - 2018 - Paper 2

Complete the Venn diagram for this information.

Find the probability that the number is a member of A ∩ B.

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