Question

We know 20% of groceries in a store are non gluten & 90 % have no nuts. If the use of nuts & gluten are not linked what portion of the grocery products will have at least 1 of these two allergens

Answer 1

The use of nuts and gluten are not linked means they are two independent events. For independent events A and B, P(A and B) = P(A) x P(B)

P(non gluten) = 0.20

P(no nuts) = 0.90

P(no gluten and no nuts) = 0.20 x 0.90 = 0.18

P(the grocery products will have at least 1 of these two allergens) = 1 - P(no gluten and no nuts)

= 1 - 0.18

= 0.82