Probability II: Mutually Exclusive & Independent Events
IB Mathematics AA · SL & HL · Shadow Worksheet
Practice
Question 1
Events A and B are mutually exclusive with \(P(A)=0.3\) and \(P(B)=0.5\). Find:
(a)\(P(A\cup B)\)
(b)\(P(A\cap B)\)
(c)\(P(A'\cap B')\)
(b)
Answer
\(0\) (mutually exclusive)
Question 2
Events A and B are independent with \(P(A)=0.4\) and \(P(B)=0.6\). Find:
(a)\(P(A\cap B)\)
(b)\(P(A\cup B)\)
(c)\(P(A'\cap B)\)
(c)
Independence
\(P(A')\cdot P(B)=0.6\times0.6\)
Question 3
Determine whether A and B are independent, mutually exclusive, both, or neither, given \(P(A)=0.5\), \(P(B)=0.4\), \(P(A\cap B)=0.2\).
Check independence
\(P(A)\times P(B)=0.2=P(A\cap B)\) ✓ — Independent
Check mutually exclusive
\(P(A\cap B)=0.2
eq0\) — Not mutually exclusive
Answer
Independent but not mutually exclusive
Question 4
A bag contains 4 red and 6 blue balls. Two balls are drawn with replacement. Find the probability that:
(a)Both are red
(b)Different colours
(c)At least one blue
(a)
Answer
\(\tfrac{4}{10}\times\tfrac{4}{10}=\tfrac{4}{25}\)
(b)
RB or BR
\(2\times\tfrac{4}{10}\times\tfrac{6}{10}=\tfrac{12}{25}\)
(c)
Complement
\(1-P(\text{both red})=1-\tfrac{4}{25}\)
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