Adiner 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)

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

let soccer = x and golf = y

part a

1st equation: x + y = 125

2nd equation: x = y +45

part b

replace x in the 1st equation with the 2nd one:

y + 45 + y = 125

simplify:

2y + 45 = 125

subtract 45 from each side:

2y = 80

divide both sides by 2:

y = 80/2

y = 40

she plays golf for 40 minutes.

part c

no because she plays soccer for 45 minutes longer than golf 40 +45 =   85 minutes, not 80 minutes.

english, cause i can’t you