Question

Out of six computer chips, two are defective. If two chips are randomly chosen for testing (without replacement), compute the probability that both of them are defective. List all the outcomes in the sample space.

Answer 1

Answer:

The probability that of the two chips selected both are defective is 0.1089.

Step-by-step explanation:

Let X = number of defective chips.

It is provided that there are 2 defective chips among 6 chips.

The probability of selecting a defective chip is:

$P(X)=p=\frac{2}{6}=0.33$

A sample of n = 2 chips are selected.

The random variable X follows a Binomial distribution with parameter n = 2 and p = 0.33.

The probability function of a Binomial distribution is:

$P(X=x)={n\choose x}p^{x}(1-p)^{n-x};\ x=0, 1, 2, ...$

Compute the probability that of the two chips selected both are defective as follows:

$P(X=2)={2\choose 2}(0.33)^{2}(1-0.33)^{2-2}=1\times 0.1089\times 1=0.1089$

Thus, the probability that of the two chips selected both are defective is 0.1089.

The sample space of selecting two chips is:

S = (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)

     (2, 1),  (2, 3), (2, 4), (2, 5), (2, 6)

     (3, 1), (3, 2), (3, 4), (3, 5), (3, 6)

     (4, 1), (4, 2), (4, 3), (4, 5), (4, 6)

     (5, 1), (5, 2), (5, 3), (5, 4), (5, 6)

     (6, 1), (6, 2), (6, 3), (6, 4), (6, 5)