It is known that 10% of the calculators shipped from a particular factory are defective. What is the probability that at least one in a random sample of four calculators is defective?

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It is known that 10% of the calculators shipped from a particular factory are defective. What is the probability that at least one in a random sample of four calculators is defective?

**Homework Question 5 for Exam 2 Review**

**Question 5:**

It is known that 10% of the calculators shipped from a particular factory are defective. What is the probability that at least one in a random sample of four calculators is defective?

**Multiple Choice Options:**

- (A) 0.0010
- (B) 0.2916
- (C) 0.3439
- (D) 0.6561

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Note: This homework question is provided by McGraw Hill Education.

**Explanation:**

To solve this problem, use the complement rule of probability. Calculate the probability that none of the calculators are defective and subtract it from 1 to find the probability that at least one is defective.

Let \( p = 0.10 \) be the probability that a calculator is defective. The probability that a calculator is not defective is \( 1 - p = 0.90 \).

For four calculators, the probability that none are defective is \( 0.90^4 \).

Therefore, the probability that at least one is defective is \( 1 - 0.90^4 \).
Transcribed Image Text:**Homework Question 5 for Exam 2 Review** **Question 5:** It is known that 10% of the calculators shipped from a particular factory are defective. What is the probability that at least one in a random sample of four calculators is defective? **Multiple Choice Options:** - (A) 0.0010 - (B) 0.2916 - (C) 0.3439 - (D) 0.6561 **Navigation:** - Prev (Previous question): Question 4 of 90 - Next (Next question): Question 6 of 90 **Additional Resources:** - eBook - Print - References Note: This homework question is provided by McGraw Hill Education. **Explanation:** To solve this problem, use the complement rule of probability. Calculate the probability that none of the calculators are defective and subtract it from 1 to find the probability that at least one is defective. Let \( p = 0.10 \) be the probability that a calculator is defective. The probability that a calculator is not defective is \( 1 - p = 0.90 \). For four calculators, the probability that none are defective is \( 0.90^4 \). Therefore, the probability that at least one is defective is \( 1 - 0.90^4 \).
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