Sets 3
4 marks · HardIn a club, every member either plays table tennis (T), badminton (B), or both. There are 60 members in total. 42 members play table tennis, 28 play badminton, and members play both.
Given that a member is chosen at random and is known to play table tennis, the probability that they also play badminton is .
Express the number of members who play both sports in terms of the information above.
Find the value of .
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(a) so
(b) 12
Common mistakes: Mixing up numerator/denominator in conditional probability
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Marking points
M1 (a) · 1 mark · Writes expression for conditional probability using set notation:
A1 (a) · 1 mark · Correctly expresses
M1 (b) · 1 mark · Calculates or equivalent working (follow-through)
A1 (b) · 1 mark · Final answer (follow-through)
Worked solution
P(B|T) = n(B ∩ T) / n(T) = 2/7
n(T) = 42. So n(B ∩ T) = (2/7) × 42 = 2 × 6 = 12.