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?

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%.

< coa = 150 ( given)

as ba and bc are tangents

so oc and oa is perpendicular to cb and ab respectively because in circle normal passes through centre

so in quadrilateral oabc

< coa + < oab + < ocb + < abc = 360

150 +90+90 + < abc = 360

330 + < abc = 360

< abc = 360 -330 = 30

so < abc = 30

⭐dhruv⭐

x = 3 ± √(5+y)