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.

It is given in the question that,

Probability of failure = x

And, probability of success = 2x

∴ x + 2x = 1

3x = 1

∴

Let us now assume

Also, X be the random variable that represents the number of trials

Hence, by binomial distribution we have:

∴ Probability of having at least 4 successes

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