The probabilities of events A, B and C are related, as shown in the Venn diagram below - AQA - A-Level Maths Pure - Question 10 - 2020 - Paper 3
Question 10
The probabilities of events A, B and C are related, as shown in the Venn diagram below.
$\varepsilon$
A
0.12
B
0.05
0.18
0.30
C
0.24
Find the value of x.
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Worked Solution & Example Answer:The probabilities of events A, B and C are related, as shown in the Venn diagram below - AQA - A-Level Maths Pure - Question 10 - 2020 - Paper 3
Step 1
Find the total probability in the Venn diagram
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Answer
The total probability for all events A, B, and C (including overlap) must equal 1. We can summarize what we have in the Venn diagram:
P(A)+P(B)+P(C)+P(A∩B)+P(B∩C)+P(C∩A)+P(A∩B∩C)+x=1
Where:
P(A)=0.12 (only A)
P(B)=0.05 (only B)
P(C)=0.24 (only C)
P(A∩B)=0.18
P(B∩C)=0.30
Plugging in these values:
0.12+0.05+0.24+0.18+0.30+x=1
Step 2
Calculate the remaining probability for x
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Answer
Adding the known probabilities:
0.12+0.05+0.24+0.18+0.30=0.89
So we have:
0.89+x=1
Subtracting 0.89 from both sides gives:
x=1−0.89x=0.11
Step 3
Circle your answer
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Answer
The value of x is 0.11. The correct answer to circle is:
