#### Question

An experiment succeeds twice as often as it fails. Find the probability that in the next six trials, there will be at least 4 successes.

#### Solution

The probability of success is twice the probability of failure.

Let the probability of failure be *x*.

∴ Probability of success = 2*x*

Let X be the random variable that represents the number of successes in six trials.

By binomial distribution, we obtain

P (X = *x*) = `""^nC_x P^(n-x) q^x`

Probability of at least 4 successes = P (X ≥ 4)

= P (X = 4) + P (X = 5) + P (X = 6)

Is there an error in this question or solution?

Solution An Experiment Succeeds Twice as Often as It Fails. Find the Probability that in the Next Six Trials, There Will Be at Least 4 Successes. Concept: Bernoulli Trials and Binomial Distribution.