Question

A balloon artist claims the probability a randomly selected balloon pops while being molded is 0.10 and that balloons pop independent of other balloons. Part A. If we select a random sample of 3 balloons, what’s the probability that all of them pop while being molded?

Answer 1

Answer: 0.001

Work Shown:

(0.10)^3 = (0.10)*(0.10)*(0.10) = 0.001

Answer 2

0.001

Explanation:

This can be modeled as a binomial distribution as:

• There is a fixed number (n) of trials
• Each trial is either a success or failure
• All trials are independent
• The probability of success (p) is the same in each trial
• The variable is the total number of successes in the n trials

Let "success" be the balloon popping.

⇒ trials (n) = 3

⇒ probability of success (p) = 0.10

To find the probability that all 3 of the balloons pop, use the binomial distribution with x = 3:

`\begin{aligned} \displaystyle P(X=x) & =\binom{n}{x} \cdot p^x \cdot (1-p)^(n-x)\\\\\implies P(X=3) & =\binom{3}{3} \cdot 0.1^3 \cdot (1-0.1)^(3-3)\\ & = 1 \cdot 0.001 \cdot 1\\ & =0.001 \end{aligned}`