Question

Find The probability of no failures in five trials of a binomial experiment in which the probability of success is 30%.

Answer 1

If the probability of success is 30%, then p=0.3 and q=1-p=1-0.3=0.7.

The probability of no failures in five trials in binomial experiment is

$C_5^5 p^5q^{5-5}=C_5^5 (0.3)^5(0.7)^{5-5}=(0.3)^5=0.00243$.

In percent this is 0.00243·100%=0.243%=0.2% (rounded to the nearest tenth of a percent).

Answer: The probability of no failures in five trials is 0.2%.