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.

The probability of success is twice the probability of failure.

Let the probability of failure be x.

∴ Probability of success = 2x

Let p = and q =

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

By binomial distribution, we obtain

P (X = x) =

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

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