A certain type of new business succeeds 70% of the time. Suppose that four such businesses open (where they do not compete with each other, so it is reasonable to believe that their relative successes would be independent). The probability that all four businesses fail is?
Let's represent success as S and failure as F. Since the probability of success is 70%, the probability of failure is 30%.
Therefore, the probability that all four businesses fail is:
P(F) x P(F) x P(F) x P(F)
= 0.3 x 0.3 x 0.3 x 0.3
= 0.3^4
= 0.0081
So, the probability that all four businesses fail is 0.81%.