Given the universal set $Z = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}$, sets are defined as: - $A = \{1, 5, 6, 8, 9\}$ - $B = \{2, 6, 9\}$ (a) Complete the Venn diagram to represent this information. (b) A number is chosen at random from the universal set $Z$. Find the probability that the number is in the set $A \cap B$.

GCSE Edexcel Maths Simple & Compound Interest, Growth & Decay: Given the universal set $Z = \{1

Given the universal set $Z = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}$, sets are defined as: - $A = \{1, 5, 6, 8, 9\}$ - $B = \{2, 6, 9\}$ (a) Complete the Venn diagram to represent this information - Edexcel - GCSE Maths - Question 2 - 2019 - Paper 3

Question 2

$Given-the-universal-set-$Z-=-\{1,-2,-3,-4,-5,-6,-7,-8,-9\}$,-sets-are-defined-as:---$A-=-\{1,-5,-6,-8,-9\}$---$B-=-\{2,-6,-9\}$--(a)-Complete-the-Venn-diagram-to-represent-this-information-Edexcel-GCSE Maths-Question 2-2019-Paper 3.png$

Given the universal set $Z = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}$, sets are defined as: - $A = \{1, 5, 6, 8, 9\}$ - $B = \{2, 6, 9\}$ (a) Complete the Venn diagram to rep... show full transcript

Worked Solution & Example Answer:Given the universal set $Z = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}$, sets are defined as: - $A = \{1, 5, 6, 8, 9\}$ - $B = \{2, 6, 9\}$ (a) Complete the Venn diagram to represent this information - Edexcel - GCSE Maths - Question 2 - 2019 - Paper 3

Step 1

Complete the Venn diagram

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Answer

To complete the Venn diagram:

Identify the elements present in both sets A and B. The only common element is 6. Place 6 in the intersection.
Fill in the elements of set A: Remaining elements are 1, 5, 8, and 9.
For set B, after placing 6 in the intersection, the remaining elements are 2 and 9.

The final placement should be:

In set A: {1, 5, 8, 9}
In set B: {2}
In the intersection (A ∩ B): {6}

This represents the complete distribution of elements in the Venn diagram.

Step 2

Find the probability that the number is in the set A ∩ B

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Answer

To find the probability that a number chosen at random from the universal set $Z$ is in the set $A \cap B$ :

The intersection $A \cap B = \{6\}$ has 1 element.
The total number of elements in the universal set $Z$ is 9.
The probability is calculated as:

$P(A \cap B) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{1}{9}$

Thus, the probability that the selected number is in the set $A \cap B$ is $rac{1}{9}$ .

Given the universal set $Z = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}$, sets are defined as: - $A = \{1, 5, 6, 8, 9\}$ - $B = \{2, 6, 9\}$ (a) Complete the Venn diagram to represent this information - Edexcel - GCSE Maths - Question 2 - 2019 - Paper 3

Worked Solution & Example Answer:Given the universal set $Z = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}$, sets are defined as: - $A = \{1, 5, 6, 8, 9\}$ - $B = \{2, 6, 9\}$ (a) Complete the Venn diagram to represent this information - Edexcel - GCSE Maths - Question 2 - 2019 - Paper 3

Complete the Venn diagram

Find the probability that the number is in the set A ∩ B

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