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Worksheet
Probability I: Venn Diagrams
IB Mathematics AA · SL & HL · Shadow Worksheet
Practice
Name
Question 1
In a class of 30 students, 18 study French (F), 15 study Spanish (S), and 7 study both. Draw a Venn diagram and find:
(a)How many study at least one language.
(b)How many study neither.
(c)\(P( ext{French only})\)
(a)
Inclusion-exclusion
\(18+15-7=26\)
Answer
26 students
(b)
Answer
\(30-26=4\) students
(c)
French only \(=18-7=11\)
Answer
\(\dfrac{11}{30}\)
Question 2
Events A and B satisfy \(P(A)=0.5\), \(P(B)=0.4\), \(P(A\cup B)=0.7\). Find \(P(A\cap B)\) and draw a Venn diagram with all regions labelled.
Inclusion-exclusion
\(P(A\cap B)=P(A)+P(B)-P(A\cup B)=0.5+0.4-0.7\)
Answer
\(P(A\cap B)=0.2\); Venn regions: A only 0.3, B only 0.2, both 0.2, neither 0.3
Question 3
The Venn diagram shows probabilities for events A and B: \(P(A ext{ only})=0.4\), \(P(A\cap B)=0.15\), \(P(B ext{ only})=0.25\). Find:
(a)\(P(A)\)
(b)\(P(B)\)
(c)\(P(A'\cap B')\)
(a)
Answer
\(0.55\)
(b)
Answer
\(0.40\)
(c)
Neither region
\(1-0.4-0.15-0.25\)
Answer
\(0.20\)
Question 4
In a survey: 60% own a car (C), 40% own a bike (B), 15% own both. A person is chosen at random.
(a)\(P(C\cup B)\)
(b)\(P( ext{car only})\)
(c)\(P(C'\cap B')\)
(a)
Answer
\(0.85\)
(b)
Answer
\(0.45\)
(c)
Answer
\(0.15\)
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