Question 1199248: Q1) A pizza shop offers three toppings: pineapple, peppers, and pepperoni. A pizza can have
0, 1, 2, or 3 toppings. What’s the probability that a random customer asks for two toppings?
Found 2 solutions by greenestamps, math_tutor2020:
Answer by greenestamps(13203)   (Show Source):
Answer by math_tutor2020(3817)  (Show Source):
You can put this solution on YOUR website!
Let's flip 3 coins.
H = heads = you order a certain topping
T = tails = do not order a certain topping
HHH for instance means you get 3 toppings
HHT means you'd only get 2 toppings
and so on.
Here are all of the ways to flip 3 coins.
It is the sample space.
HHH
HHT
HTH
THH
TTH
THT
HTT
TTT
I've broken up that list such that each block represents a different count of H's and T's
The second block has exactly 2 H's and 1 T
The third block has exactly 1 H and 2 T's
There are 2^3 = 8 ways to flip 3 coins. There are 8 items in that sample space above.
Of those 8 ways, there are 3 items that have two toppings show up:
HHT
HTH
THH
The order of the toppings doesn't matter so effectively these are all the same. All that matters is that we have two heads in there somewhere.
We have 3 ways to get what we want (have exactly two toppings) out of 8 ways to order 0,1,2, or 3 toppings.
Therefore, we arrive at the final answer 3/8 to represent the probability of a random customer getting two toppings.
Keep in mind that this assumes each of the items in the sample space is equally likely.
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