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 succeed is?
To find the probability that all four businesses succeed, we need to multiply the individual probabilities of success for each business.
Since each business has a 70% chance of succeeding, the probability of success for each business is 0.70.
Therefore, the probability that all four businesses succeed is:
0.70 * 0.70 * 0.70 * 0.70 = 0.70^4 = 0.2401
So, the probability that all four businesses succeed is 24.01%.