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.

The probability of at least one failure in five trials of a binomial experiment in which the probability of success is 30% is 0.243%.

What is a Binomial distribution?

A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,

P(x) = ⁿCₓ (pˣ) (q⁽ⁿ⁻ˣ⁾)

Where,

x is the number of successes needed,

n is the number of trials or sample size,

p is the probability of a single success, and

q is the probability of a single failure.

The probability of at least one failure in five trials of a binomial experiment is equal to the probability of 5 successes in five trials. Therefore, the probability can be written as,

P(X=5) = ⁵C₅ (0.3)⁵ (0.7)⁰

= 1 × (0.3)⁵ × 1

= 0.00243

= 0.243%

Hence, the probability of at least one failure in five trials of a binomial experiment in which the probability of success is 30% is 0.243%.

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