contestada

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?

Respuesta :

Answer:

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%.

Otras preguntas