Mathematicalnumber
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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?

Sagot :

Answer:  0.001

Work Shown:

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

semsee45

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]

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