A diner has collected data about customer coffee-drinking habits. They have calculated that P(cream)=0.5, P(sugar)=0.6, and P(cream or sugar)=0.7. What is P(cream and sugar).

Answer 1

If A and B are events, then

P(A or B) = P(A) + P(B) - P(A and B)

Let A be cream, B be sugar:

Using the formula:

P(cream or sugar) = P(cream) + P(sugar) - P(cream and sugar)

0.7 = 0.5 + 0.6 - P(cream and sugar)

-0.4 = -P(cream and sugar)

0.4 = P(cream and sugar)