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 at least two businesses succeeds is?
0.856
0.766
0.865
0.916
0.996
To find the probability that at least two businesses succeed, we can calculate the probability that exactly one business fails and subtract that from 1.
The probability that one business fails is 0.3, and the probability that the other three succeed is 0.7^3 = 0.343. So, the probability that exactly one business fails is 0.3 * 0.343 = 0.1029.
Therefore, the probability that at least two businesses succeed is 1 - 0.1029 = 0.9971.