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

GCSE Edexcel Maths Coordinate Geometry: 1. Let $ar{E} = \{ \text{even n

1. Let $ar{E} = \{ \text{even numbers between 1 and 25} \}$ $A = \{ 2, 8, 10, 14 \}$ $B = \{ 6, 8, 20 \}$ $C = \{ 6, 18, 20, 22 \}$ (a) Complete the Venn diagram for this information - Edexcel - GCSE Maths - Question 3 - 2018 - Paper 2

Question 3

$1.-Let-$ar{E}-=-\{-\text{even-numbers-between-1-and-25}-\}$----$A-=-\{-2,-8,-10,-14-\}$----$B-=-\{-6,-8,-20-\}$----$C-=-\{-6,-18,-20,-22-\}$-----(a)-Complete-the-Venn-diagram-for-this-information-Edexcel-GCSE Maths-Question 3-2018-Paper 2.png$

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

Worked Solution & Example Answer:1. Let $ar{E} = \{ \text{even numbers between 1 and 25} \}$ $A = \{ 2, 8, 10, 14 \}$ $B = \{ 6, 8, 20 \}$ $C = \{ 6, 18, 20, 22 \}$ (a) Complete the Venn diagram for this information - Edexcel - GCSE Maths - Question 3 - 2018 - Paper 2

Step 1

Complete the Venn diagram for this information.

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Answer

To complete the Venn diagram, we first need to identify the numbers in each set:

Set A contains: 2, 8, 10, 14
Set B contains: 6, 8, 20
Set C contains: 6, 18, 20, 22

Now let's determine the overlaps:

A and B: The common number is 8.
A and C: There are no common numbers.
B and C: The common numbers are 6 and 20.
A, B, and C: There are no common numbers among all three sets.

The completed Venn diagram should have:

In circle A: 2, 10, 14 (with 8 in the overlap with B)
In circle B: 6 (with 8 in the overlap with A and 20 in the overlap with C)
In circle C: 18, 22 (with 6 and 20 in overlaps with B)
The central region where all three overlap is empty.

Thus, the completed Venn diagram shows the numbers positioned correctly based on their memberships in the respective sets.

Step 2

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

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Answer

To calculate the probability that a randomly chosen number from $ar{E}$ is a member of $A \cap B$ :

Identify members of $A \cap B$ : The only member common to both A and B is 8.
Determine the total number of even numbers in $ar{E}$ : The even numbers between 1 and 25 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24. This gives us a total of 12 even numbers.
Calculate the probability: The probability P that a number is in $A \cap B$ is calculated as: $P(A \cap B) = \frac{\text{Number of elements in } A \cap B}{\text{Total number of elements in } \bar{E}} = \frac{1}{12}$

Hence, the probability is $rac{1}{12}$ .

1. Let $ar{E} = \{ \text{even numbers between 1 and 25} \}$ $A = \{ 2, 8, 10, 14 \}$ $B = \{ 6, 8, 20 \}$ $C = \{ 6, 18, 20, 22 \}$ (a) Complete the Venn diagram for this information - Edexcel - GCSE Maths - Question 3 - 2018 - Paper 2

Worked Solution & Example Answer:1. Let $ar{E} = \{ \text{even numbers between 1 and 25} \}$ $A = \{ 2, 8, 10, 14 \}$ $B = \{ 6, 8, 20 \}$ $C = \{ 6, 18, 20, 22 \}$ (a) Complete the Venn diagram for this information - Edexcel - GCSE Maths - Question 3 - 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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1. Let $ar{E} = \{ \text{even numbers between 1 and 25} \}$ $A = \{ 2, 8, 10, 14 \}$ $B = \{ 6, 8, 20 \}$ $C = \{ 6, 18, 20, 22 \}$ (a) Complete the Venn diagram for this information - Edexcel - GCSE Maths - Question 3 - 2018 - Paper 2

Worked Solution & Example Answer:1. Let $ar{E} = \{ \text{even numbers between 1 and 25} \}$ $A = \{ 2, 8, 10, 14 \}$ $B = \{ 6, 8, 20 \}$ $C = \{ 6, 18, 20, 22 \}$ (a) Complete the Venn diagram for this information - Edexcel - GCSE Maths - Question 3 - 2018 - Paper 2