Question

Suppose that a computer chip company has just shipped computer chips to a computer company.​ Unfortunately, of the chips are defective. ​(a) Compute the probability that two randomly selected chips are defective using conditional probability. ​(b) The probability that the first randomly selected chip is defective is . Compute the probability that two randomly selected chips are defective under the assumption of independent events. ​(a) The probability is nothing. ​(Round to eight decimal places as​ needed.)

Answer 1

Answer:

(a) 0.0000245

(b) 0.000025

Step-by-step explanation:

The complete question is:

Suppose that a computer chip company has just shipped 10,000 computer chips to a computer company. Unfortunately, 50 of the chips are defective. (a) Compute the probability that two randomly selected chips are defective using conditional probability. (b) There are 50 defective chips out of 10,000 shipped. The probability that the first chip randomly selected is defective is  50 /10,000  = 0.005.  Compute the probability that two randomly selected chips are defective under the assumption of independent events.

Solution:

(a)

In this case we need to compute the conditional probability of selecting two defective chips, i.e. the selection of the second defective chip is dependent on the first defective chip.

The probability of selecting the first defective chip is:

$P(1D)=\frac{50}{10000}=0.005$

Now there are 9999 chips left and 49 defective chips among them.

The probability of selecting the second defective chip is:

$P(2D)=\frac{49}{9999}=0.0049$

Compute the probability that two randomly selected chips are defective using conditional probability as follows:

P (Two defective chips) $=P(1D)\times P(2D)=0.005\times 0.0049=0.0000245$

Thus, the answer is 0.0000245.

(b)

Compute the probability that two randomly selected chips are defective under the assumption of independent events as follows:

The above statement implies that the selection was done with replacement.

The probability is:

P (Two defective chips) $=P(1D)\times P(2D)$

                                      $=\frac{50}{10000}\times \frac{50}{10000}\\\\=0.005\times 0.005\\\\=0.000025$

Thus, the probability that two randomly selected chips are defective under the assumption of independent events is 0.000025.