Question

You are ordering a hamburger and can get up to 88 toppings, but each topping can only be used once. You tell the cashier to surprise you with the toppings you get. What is the probability that you get 33 toppings? Express your answer as a fraction or a decimal number rounded to four decimal places.

Answer 1

Let X be the number of toppings you get out of 88. Considering each topping is equally likely to be added or not we get that probability of a topping being added = 1/2

Then X ~ Binomial (88,1/2) where the probabiliy of success is probability of a topping being added = p = 1/2

P(X = k) can be computed as: We first choose k toppings out of 88 in   ways and then multiply this by the probability that all k chosen are added = (p)^k [as addition of different toppings is independent] and then we multiply it by the probability that the rest are not added = (1-p)^(88-k) to ensure that exactly k of them are added.

So,

   with p = 1/2

We need to find P(X = 33) so,

= 0.054 (rounded to four decimal places)

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