The probability of at least 5 successes in the six trials of this experiment?

Question

An experiment succeeds twice as often as its fails.the probability of at least 5 successes in the six trials of this experiment?

Answer 1

The ratio of successes to failures is 2:1 so the probability p of failure is 1/3. (1/3+2/3)^6=1.

The probability of 5 successes out of 6 is 6p(1-p)^5 (one failure and 5 successes) and of 6 successes is (1-p)^6. Add these together: (1-p)^5(6p+1-p)=(1-p)^5(5p+1)=(2/3)^5(8/3)=256/729=0.3512 approx or 35.12%, which is the probability of at least 5 successes.