A certain type of new business succeeds 60% of the time. Suppose that three 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 exactly one business succeeds is?
0.3624
0.0756
0.2880
0.4182
To calculate the probability that exactly one business succeeds out of three, we need to consider the three possible scenarios:
1. Business 1 succeeds, Business 2 fails, Business 3 fails.
2. Business 1 fails, Business 2 succeeds, Business 3 fails.
3. Business 1 fails, Business 2 fails, Business 3 succeeds.
The probability of success for each business is 0.6, and the probability of failure is 0.4.
The probability of scenario 1 is:
(0.6)(0.4)(0.4) = 0.096
The probability of scenario 2 is:
(0.4)(0.6)(0.4) = 0.096
The probability of scenario 3 is:
(0.4)(0.4)(0.6) = 0.096
Adding these probabilities together gives us the total probability that exactly one business succeeds:
0.096 + 0.096 + 0.096 = 0.288
Therefore, the probability that exactly one business succeeds is 0.288, which is closest to 0.2880.