A factory tests a random sample of 23 transistors for defects. The probability that a particular transistor will be defective has been established by past experience as 0.03. What is the probability that there are no defective transistors in the? sample?

The probability that a particular transistor be deflective is 0.03. This situation may be seen as a experiment-result situation. You may choose one of the transistors and find out if it is deflective.

Be r the probability that a transistor selected be deflective. Be R the probability that the transistor selected don't be deflective; it is easy to note that R=1-0.03, due to the total of possibilities for the single experiment are two: deflective or not deflective.

If a single result has a probability of p, the probability P that the same result be obtained n times is:

[tex]P=p^{n}[/tex]

So, the probability that none of the transistors be deflective is:

[tex]P=0.97^{23}=0.496[/tex]