Let PZ 045 P Y 042 and Use a Venn diagram to find a Soluti

Let P(Z) = 0.45, P (Y) =0.42, and . Use a Venn diagram to find (a)

Solution

a)
P(Z) = 0.45
P(Z\') = 1 - 0.45 = 0.55
P(Y) = 0.42
P(Y\') = 1 - 0.42 = 0.58

P( Z \' n Y\') = 1 - P( Z u Y) = 1 - 0.45 - 0.42 + 0.18 = 0.31

b)
P( Z \' U Y\') = 1 - P( Z n Y) = 1 - 0.18 = 0.82

c)
P(Z\' U Y) = P(Z\') + P(Y) - P(Z\' n Y) = 0.55 + 0.42 - P( Y Only) = 0.55 + 0.42 - 0.26 = 0.71