The general addition rule for three events states that P (A or B or C) = P (A) + P (B) + P (C) - P (A and B) - P (A and C) - P (B and C) + P (A and B and C). A new magazine publishes columns entitled "Art" (A), "Books" (B), and "Cinema" (C). Suppose that 15% of all subscribers read A 23% read B 34% read C 8% read A and B 9% read A and C 13% read B and C 5% read all three columns. What is the probability that a randomly selected subscriber reads at least one of these three columns?

Question

Mathematics

Nicolas Savage

6 May, 08:15

The general addition rule for three events states that P (A or B or C) = P (A) + P (B) + P (C) - P (A and B) - P (A and C) - P (B and C) + P (A and B and C). A new magazine publishes columns entitled "Art" (A), "Books" (B), and "Cinema" (C). Suppose that 15% of all subscribers read A 23% read B 34% read C 8% read A and B 9% read A and C 13% read B and C 5% read all three columns. What is the probability that a randomly selected subscriber reads at least one of these three columns?

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Answers (1)

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Sean Forbes · Answer 1

47%

Step-by-step explanation:

Here, A represents Art, B represents Books and C represents Cinema,

According to the question,

P (A) = 15% = 0.15,

P (B) = 23% = 0.23,

P (C) = 34% = 0.34,

P (A ∩ B) = 8% = 0.08

P (B ∩ C) = 13% = 0.13

P (C ∩ A) = 9% = 0.09

P (A ∩ B ∩ C) = 5% = 0.05,

We know that,

P (A ∪ B ∪ C) = P (A) + P (B) + P (C) - P (A ∩ B) - P (B ∩ C) - P (C ∩ A) + P (A ∩ B ∩ C)

= 0.15 + 0.23 + 0.34 - 0.08 - 0.13 - 0.09 + 0.05

= 0.47

= 47%

Hence, the probability that a randomly selected subscriber reads at least one of these three columns would be 47%.