Answer:
(a) The probability of exactly 2 defective PS4s among them is 0.3125.
(b) The probability that exactly 2 are defective given that at least 2 purchased PS4s are defective is 0.3846.
Step-by-step explanation:
Let <em>X</em> = number of defective PS4s.
It is provided that 4 PS4s of 8 are defective.
The probability of selecting a defective PS4 is:
A customer bought <em>n</em> = 5 PS4s.
The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> = 5 and <em>p</em> = 0.50.
The probability function of a Binomial distribution is:
(a)
Compute the probability of exactly 2 defective PS4s among them as follows:
Thus, the probability of exactly 2 defective PS4s among them is 0.3125.
(b)
Compute the probability that exactly 2 are defective given that at least 2 purchased PS4s are defective as follows:
The value of P (X = 2) is 0.3125.
The value of P (X ≥ 2) is:
Then the value of P (X = 2 | X ≥ 2) is:
Thus, the probability that exactly 2 are defective given that at least 2 purchased PS4s are defective is 0.3846.