Answer to Question #317708 in Statistics and Probability for Student2014_

Question

The probability that a randomly selected family in South Africa watches Isidingo is 0.53 and the probability that they watch Grey’s Anatomy is 0.87, whereas the probability that they watch both Isidingo and Grey’s Anatomy is 0.46. The probability that a randomly selected family watches neither Isidingo nor Grey’s Anatomy is

The probability that a randomly selected family in South Africa watches Isidingo is 0.53 and the probability that they watch Grey’s Anatomy is 0.87, whereas the probability that they watch both Isidingo and Grey’s Anatomy is 0.46. The probability that a randomly selected family watches neither Isidingo nor Grey’s Anatomy is?

Answer 1

$Inclusion-exclusion\,\,principle:\\P\left( A \right) =0.53-Isidingo\\P\left( B \right) =0.87-Anatomy\\P\left( A\cap B \right) =0.46\\P\left( A\cup B \right) =P\left( A \right) +P\left( B \right) -P\left( A\cap B \right) =0.53+0.87-0.46=0.94\\P\left( \bar{A}\cap \bar{B} \right) =1-P\left( A\cup B \right) =1-0.94=0.06$