Question 1

Suppose a business is analyzing the probability that none of its 10 randomly selected products are defective, given that the probability a single product is not defective is 0.85. Which formula correctly calculates this probability?

Accepted Answer

$$P(X = 0) = 0.85$$^{10}$$

Question 2

Given $$P(X = 0) = 0.85$$^{10}$$ = 0.1969$$, what does $$X$$ most likely represent in a business context?

Accepted Answer

The number of defective products in a sample of 10, where $$X = 0$$ means no defective products

Question 3

If the probability that a single product is not defective is 0.85, what is the probability that all 10 products in a sample are not defective?

Accepted Answer

$$0.85^{10}$$

Question 4

A company tests 10 products. If the probability that a product is defective is 0.15, what is the probability that none are defective?

Accepted Answer

$$0.85^{10}$$

Question 5

Which of the following best describes the type of probability distribution used in $$P(X = 0) = 0.85$$^{10}$$?

Accepted Answer

Binomial distribution with $$n = 10$$ and $$p = 0.85$$

Question 6

If $$P(X = 0) = 0.1969$$ for $$n = 10$$ and $$p = 0.85$$, what is the probability that at least one product is defective?

Accepted Answer

$$1 - 0.1969$$

Question 7

A business wants to reduce the probability that all 10 products are non-defective. Which of the following would decrease $$P(X = 0)$$?

Accepted Answer

Decrease the probability that a single product is not defective

Question 8

If the probability that a single product is not defective increases to 0.90, what happens to $$P(X = 0)$$ for $$n = 10$$?

Accepted Answer

$$P(X = 0)$$ increases

Question 9

Which of the following real-world scenarios can be modeled by $$P(X = 0) = 0.85$$^{10}$$?

Accepted Answer

The probability that all 10 randomly selected customers are satisfied, given each has an 85% satisfaction rate

Question 10

If $$P(X = 0) = 0.1969$$ for $$n = 10$$ and $$p = 0.85$$, which of the following is the correct interpretation?

Accepted Answer

There is a 19.69% chance that all 10 products are not defective

Probability in Binomial Distribution: Calculating $P(X=0)$

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