Let x be the number of successes throughout n independent repetitions of a random experiment having probability of success p=1/4. determine the smallest value of n so that p (1=0.7

To answer problems like this you have to use binomial:

P (x > 1) = 1 - p (0 < x. 7

So:

1 - p (0) - p (1) >.7

1 - (3 / 4) ^n - (3 / 4) ^n (n - 1) (1 / 4) >.7

Therefore n > 5.185, and the smallest value of n so that we can satisfy the given condition is 6 (rounded up)