Answer:
0.001
Step-by-step 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:
[tex]\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}[/tex]
