Question

In: Statistics and Probability

A television factory knows that 2% of their televisions are defective. In a batch of 100...

A television factory knows that 2% of their televisions are defective. In a batch of 100 new televisions, 4 of them are inspected at random. What is the probability that 1 of them will be defective? What is the probability that they all turn out to be defective?

Expert Solution

Binomial distribution :

If 'X' is the random variable representing the number of successes, the probability of getting ‘r’ successes and ‘n-r’ failures, in 'n' trails, ‘p’ probability of success ‘q’=(1-p) is given by the probability function

A television factory knows that 2% of their televisions are defective

Probability that a television is defective : p = 2/100 = 0.02; q = 1-p = 1-0.02 = 0.98

X : Number of the televisions that are defective from the 4 randomly inspected televisions

n : Number of randomly inspected televisions = 4

Applying Binomial distribution as stated above Probability of getting ‘r’ defective televisions and ‘4-r’ non-defective televisions, in 4 televisions selected, is given by the probability function

Probability that 1 of them will be defective = P(X=1)

Probability that 1 of them will be defective = 0.07529536

probability that they all turn out to be defective = P(X=4)

probability that they all turn out to be defective = 0.00000016

orchestra answered 2 years ago

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