Question

Suppose a machine produces metal parts that contain some defective parts with probability 0.05. How many parts should be produced in order that the probability of at least one part being defective is 12 or more?

(Given log1095=1.977 and log102=0.3)

(Given log1095=1.977 and log102=0.3)

- 11
- 12
- 15
- 14

Solution

The correct options are

**C** 15

**D** 14

Probability of at least one part being defective

=1− Probability of no part defective

Probability of a part to be non-defective =1−0.05=0.95

Let n be the required number of parts to be produced.

Then, 1−(0.95)n≥12

⇒(0.95)n≤12

⇒n(log1095−2)≤log1012

⇒n≥30023

n=14,15

Probability of at least one part being defective

=1− Probability of no part defective

Probability of a part to be non-defective =1−0.05=0.95

Let n be the required number of parts to be produced.

Then, 1−(0.95)n≥12

⇒(0.95)n≤12

⇒n(log1095−2)≤log1012

⇒n≥30023

n=14,15

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