Your local godfathers pizza allows you to order pizzas by...

Your local Godfather's pizza allows you to order pizzas by number, but randomly decides whether each pizza you order will be pepperoni or cheese. The type of pizza is independent of previous pizzas and the probability that the pizza is cheese is 0.6. If you order 9 pizzas, what is the probability that at most 3 of them will be cheese pizzas? Round your answer to 4 decimal places.

Transcript

00:01 In this question, we are given that in a pizza ordering, probability of pizza is cheese is 0 .6, and that you ordered nine pizzas.

00:13 I'm going to let x be the number of pizzas out of nine that are cheese.

00:18 Now x actually follows the binomial distribution.

00:21 Let's take the look at how it follows the binomial distribution.

00:25 For the binomial distribution, there are four criteria.

00:29 The first criteria, the number of trial and is fixed and are identical.

00:34 Now in this case, the trials here are we're looking at nine pizzas and for each of these pizza we're just looking at whether it's cheese or not.

00:43 So the trial experiment here is the same.

00:47 So point number one is satisfied.

00:51 Criterion number two, each trial is independent.

00:53 So for this nine pizza, each pizza whether they are cheese or not, is independent of the other pizzas.

00:59 So point two is fulfilled.

01:04 Now third point, each trial results in one and two outcomes, success and failure.

01:09 So for each pizza, the success would be it is a cheese pizza and the failure will be it is not a cheese pizza.

01:16 So point three is fulfilled.

01:19 Now point four, the probability of success in a single trial denoted by p remains the same from trial to trial.

01:26 Now this means that the probability that a pizza is cheese, which is 0 .6 and this is the same for every pizza.

01:35 So 0 .4 is fulfilled...

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