binomial distribution

Question

Find the probability of at least one failure in five trials of a binomial experiment in which the probability of success is 30%. Round to the nearest tenth of a percent. I CANT CALCULATE THE RIGHT ANSWER

Answer 1

Whenever you see the words at least in a probability problem, it is better to go with the complement :

1 - P(X<1) which is 1 - P (X=0)

p= .7

q = .3

X = getting a failure so what you are looking is P(X>=1)

P(X=0) = C (of 5 in 0) x .7^0 *.3^5= 1*1*.3^5

Then answer is 1-.3^5 = .998

Answer 2

The probability of at least one failure (we'll call this x) would include all numbers of failure except for 0 failures.

The probability of 0 failures is that of 5 successes.

Since the probability of success is 30%, the probability of 5 successes is 0.30⁵ = 0.00243.

Moreover, the total probability of all outcomes is 1.0, so x = 1.0 - 0.00243 = 0.99757.

Expressed as a percent, this gives 99.757%, and rounding to the nearest tenth gives 99.8%.