Question

In a certain manufacturing process it is known that, on average,1 in every 100 items is defective. What is the probability that the 5th item inspected is the first defective item found?

Answer 1

Answer:

0.96% probability that the 5th item inspected is the first defective item found

Step-by-step explanation:

We have these following probabilities:

1% probability that an item is defective.

99% probability that an item is not defective.

What is the probability that the 5th item inspected is the first defective item found?

First four not defective, with a 99% probability.

Fifth defective, with a 1% probability. So

$P = (0.99)^{4}*0.01 = 0.0096$

0.96% probability that the 5th item inspected is the first defective item found

Answer 2

The probability that the 5th item inspected is the first defective item found is 0.00961

1 in every 100 items is defective.

So, the probability that an item is defective is:

$p = \frac 1{100}$

If the 5th item inspected is the first defective item found, then the first four items are not defective.

The probability that an item is not defective is calculated using the following complement rule

$q = 1 - p$

$q = 1 - \frac{1}{100}$

$q = \frac{99}{100}$

The event that the 5th item is the first defective item is represented as:

q q q q p

The probability is then calculated as:

$Pr =q^4p$

So, we have:

$Pr =(99/100)^4 \times (1/100)$

Express fractions as decimal

$Pr =0.99^4 \times 0.01$

$Pr =0.00961$

Hence, the probability is 0.00961

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