binomial distributions

Question

Find the probability of no failures in five trials of a binomial experiment in which the probability of success is 30% Round to the nearest tenth of a percent.

Answer 1

This could simply be solved without resort to formula and factorials, since the question asks for only success.

Each trial gives a probability of 0.3, so the probability of 5 independent trials giving success will be 0.3⁵

^{= 0.00243 = 0.243 %, and rounding as directed gives 0.2%}

Answer 2

The probability of no failures (5 successes, x = 5) in five trials (n = 5) of a binomial experiment (success or failure) in which the probability of success is 30% ( p = 0.3, 1 - p = 0.7).

The probability of 0 failures = the probability of 5 successes in 5 independent trials with p = 0.3

nCx * (.3^5)(.7^0) = [5!/(5!0!)]*.3^5 * 1 = .3^5 = 0.00243 = 0.2% to the nearest tenth of a percent.