Question

If p(a) = 2/3, p(b) = 4/5, and p(anb) = 3/5, what is P( AuB) ( the n is the arc shape direction, so is the u)

Answer 1

By the inclusion/exclusion principle,

$P(A\cup B) = P(A) + P(B) - P(A\cap B)$

$P(A\cup B) = \dfrac23 + \dfrac45 - \dfrac35$

$P(A\cup B) = \dfrac{10}{15} + \dfrac{12}{15} - \dfrac9{15}$

$P(A\cup B) = \boxed{\dfrac{11}{15}}$