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, we need to consider the three possible scenarios: the first business succeeds while the others fail, the second business succeeds while the other two fail, or the third business succeeds while the other two fail.
Let's calculate each scenario separately:
Scenario 1: First business succeeds, second and third businesses fail
Probability = 0.6 * 0.4 * 0.4 = 0.096
Scenario 2: Second business succeeds, first and third businesses fail
Probability = 0.4 * 0.6 * 0.4 = 0.096
Scenario 3: Third business succeeds, first and second businesses fail
Probability = 0.4 * 0.4 * 0.6 = 0.096
Now, sum up the probabilities of each scenario to get 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 corresponds to 28.8%.
So the correct answer is 0.2880.