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. Determine the P (cream and sugar).

A) 0.4

B) 0.5

C) 0.6

D) 0.7

The correct answer is:

A) 0.4

Explanation:

The probability of cream, P (C), is 0.5.

The probability of sugar, P (S), is 0.6.

The probability of cream or sugar, P (C or S), is 0.7.

The union of probabilities (probability of two items using "or") is given by the formula:

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

For our problem, we have:

P (C or S) = P (C) + P (S) - P (C and S)

Using our information above, we have:

0.7 = 0.5 + 0.6 - P (C and S)

Combining like terms, we have:

0.7 = 1.1 - P (C and S)

Subtract 1.1 from each side:

0.7 - 1.1 = 1.1 - P (C and S) - 1.1

-0.4 = - P (C and S)

Divide both sides by - 1:

-0.4/-1 = - P (C and S) / - 1

0.4 = P (C and S)