Shannon is making her daily protein smoothie She has several

Shannon is making her daily protein smoothie. She has several options for her smoothie ingredients:
Fruit: strawberry, banana, blueberry, mango, pineapple, peach
Vegetable: spinach, kale, carrot, tomato
Milk: whole, almond, soy
Protein powder: vanilla, chocolate, strawberry
She will decide upon one fruit, vegetable, milk, and protein powder choice for her smoothie. Assume that all
choices are equally likely.
a) How many different choices of smoothie does Shannon have?
b) What is the probability she chooses a smoothie with chocolate protein powder?
c) What is the probability that Shannon chooses a smoothie with banana and spinach?
d) What is the probability that she chooses a smoothie with blueberry or peach?
e) Given that Shannon chooses a whole milk smoothie, what is the probability that it does not contain
vanilla protein powder?
f) Knowing that Shannon chooses a pineapple-spinach smoothie, find the probability it also contains
almond milk.

Solution

a)

There are (6 fruits)(4 veg)(3 milk)(3 pro) = 216 smoothies possible. [answer]

b)

Each choice is independent.

Hence, as there are 3 protein powders,

P(cho protein) = 1/3 = 0.3333333 [answer]

c)

P(banana and spinach) = P(banana) P(spinach) = (1/6)(1/4) = 1/24 or 0.041666667 [answer]

d)

There are 6 fruits, 2 of them are blueberry and peach. Thus,

P(blueberry or peach) = 2/6 = 1/3 = 0.333333 [answer]

e)

Again, the events are independent for each category.

Thus, there are 3 non-vanilla proteins our of 4.

P(not vanilla|whole) = 3/4 = 0.75 [answer]

f)

Again, the events are independent for each category.

Thus, there are 3 milk options, one of which is almond.

Thus,
P(almond|pineapple, spinach) = 1/3 = 0.33333333 [answer]