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. How many different choices of smoothie does Shannon have? What is the probability she chooses a smoothie with chocolate protein powder What is the probability that Shannon chooses a smoothie with banana and spinach? What is the probability that she chooses a smoothie with blueberry or peach? Given that Shannon chooses a whole milk smoothie, what is the probability that it does not contain vanilla protein powder? Knowing that Shannon chooses a pineapple-spinach smoothie, find the probably it also contains almond milk.

Solution

a)

6 fruits*4 veg*3 milk*3 pro = 216 [answer]

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b)

There are 3 protein powders. Thus,

P(choco) = 1/3 [answer]

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c)

P(banana and spinach) = P(banana) P(spinach) = 1/6 * 1/4

=1/24 [answer]

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d)

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

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e)

milk and protein powder are independent events.

Thus, we can disregard the whole milk given,

P(not vanilla) = 2 not vanilla proteins/3 proteins = 2/3 [answer]

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f)

again, fruit and vegetable is independent of the milk, so it doesn\'t matter.

P(almond|pineapple-spinach) = P(almond) = 1/3 [answer]