Question

Judging from recent experience, 5 percent of the computer keyboards produced by an automatic, high-speed machine are defective. If six keyboards are randomly selected, what is the probability that none of the keyboards are defective?

• 0.001
• 0.167
• 0.735
• 0.500

Answer 1

Concepts and reason

A binomial distribution describes the possible number of times that a particular event will occur in a sequence of observations.

• A trial has only two possible outcomes namely success or failure.

• There is fixed number of identical trials.

• The trials of the experiment are independent of each other.

Fundamentals

The probability mass function of Binomial distribution is,

Here,

The number of trials

The probability of success

The probability of failure

From the given information we have,

Sample size

Probability of success is

Let X be the number of defective keyboards. Here

The probability mass function is given by,

Compute the probability that none of the keyboards are defective. That is,

Ans:

The probability that none of the keyboards are defective is 0.7351.