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
