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). (2 points)

Answer 1

Answer:

P(cream and sugar) = 0.4

Step-by-step explanation:

* Lets study the meaning of or , and on probability

- The use of the word or means that you are calculating the probability

 that either event A or event B happened

-  Both events do not have to happen

- The use the word and, means that both event A and B have to happen

* The addition rules are:

# P(A or B) = P(A) + P(B) ⇒ mutually exclusive (events cannot happen

 at the same time)

# P(A or B) = P(A) + P(B) - P(A and B) ⇒ non-mutually exclusive (if they

 have at least one outcome in common)

- The union is written as A∪B or “A or B”.

- The intersection is written as A∩B or “A and B”

* Lets solve the question

∵ P(cream) = 0.5

∵ P(sugar) = 0.6

∵ P(cream or sugar) = 0.7

- To find P(cream and sugar) lets use the rule of non-mutually exclusive

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

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

- Lets substitute the values of P(cream) , P(sugar) , P(cream or sugar)

 in the rule

∵ 0.7 = 0.5 + 0.6 - P(cream and sugar) ⇒ add the like terms

∴ 0.7 = 1.1 - P(cream and sugar) ⇒ subtract 1.1 from both sides

∴ 0.7 - 1.1 = - P(cream and sugar)

∴ - 0.4 = - P(cream and sugar) ⇒ multiply both sides by -1

∴ 0.4 = P(cream and sugar)

* P(cream and sugar) = 0.4

Answer 2

Answer:

0.4

Step-by-step explanation: