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).

Answer 1

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

Answer 2

Answer: P( Cream and Sugar) = 0.4

Step-by-step explanation:

Since we have given that

P(Cream)=0.5

P(Sugar)=0.6

P(Cream or Sugar)=0.7

As we know the " Probability Rules" so, we get,

$P(Cream\ and\ Sugar)=P(Cream)+P(Sugar)-P(Cream\ or\ Sugar)\\\\P(C\cap S)=P(C)+P(S)-P(C\cup S)\\\\P(C\cap S)=0.5+0.6-0.7\\\\P(C\cap S)=1.1-0.7\\\\P(C\cap S)=0.4$

So, P( Cream and Sugar) = 0.4