Answered: Mexican restaurant, six with hot…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

You order thirteen burritos to go from a Mexican restaurant, six with hot peppers and seven without. However, the restaurant forgot to label them. If you pick three burritos at random, find the probability of the given event. (Round your answer to three decimal places.)

At least two have hot peppers.

Expert Solution

Step 1

Given:

Thirteen burritos are ordered from a Mexican restaurant, six with hot peppers and seven without.

Sample size,

$n = 3$

We need to determine the probability that, if three burritos are picked at random then at least two have hot peppers.

Concept:

We use Binomial probability law to find the required probability.

If a random variable $X$ follows Binomial Distribution with parameters $n$ and $p$ then the Binomial probability law is given by;

$P (X = x) = C (n, x) p^{x} q^{(n - x)}; x = 0, 1, 2, . . ., n where C (n, x) = \frac{n!}{x! (n - x)!} n is the number of trials p is the probability of success x is the number of outcomes q = (1 - p)$