Question

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

Answer 1

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)

Answer 2

Answer: 0.4

Explanation:

Given: P(cream) = 0.5

P(sugar) = 0.6

P(cream or sugar) = 0.7

We know that to calculate probability of event A or B we apply the formula below:

`\text{P(A or B)=P(A)+P(B)-P(A and B)}\\\\\Rightarrow \text{P(A and B)=P(A)+P(B)-P(A or B)}`

`\Rightarrow\text{P(cream and sugar)= P(cream)+P(sugar) -P(cream or sugar)}\\\\\Rightarrow\text{P(cream and sugar)}=0.5+0.6-0.7 \\\\\Rightarrow\text{P(cream and sugar)}=0.4`