I have just started business school and am struggling with this HW problem. any help would be great!!...A certain type of new business succeeds 60% of the time. Suppose that 3 such businesses open (where they do not compete so its reasonable to believe that their relative successes would be independent) whats is the probability that all 3 businesses succed? the probability that all 3 fail? and the probability that at least 1 succeeds? if you could show me how you got the answer that would be great thanks sooo much!

The 3 "such businesses" should be "3 certain type of new businesses" as stated in line 2. Knowing that they succeed 60% of the time, it would be 60% chance each would succeed and 40% that each would fail. Do you agree?

Sra

To solve this problem, we will use the concept of independent events and the multiplication rule.

The given information tells us that a certain type of new business succeeds 60% of the time. Therefore, the probability of success (S) is 0.6, and the probability of failure (F) is 1 - 0.6 = 0.4.

We are asked to find the probability that all three businesses succeed, all three businesses fail, and at least one business succeeds. Let's solve each part step by step:

1. Probability that all three businesses succeed:
Since the successes or failures of the businesses are assumed to be independent, the probability that all three businesses succeed is calculated by multiplying their individual probabilities of success:

P(all 3 businesses succeed) = P(S) * P(S) * P(S) = 0.6 * 0.6 * 0.6 = 0.216 or 21.6%.

Therefore, the probability that all three businesses succeed is 0.216 or 21.6%.

2. Probability that all three businesses fail:
Similarly, the probability that all three businesses fail can be calculated by multiplying their individual probabilities of failure:

P(all 3 businesses fail) = P(F) * P(F) * P(F) = 0.4 * 0.4 * 0.4 = 0.064 or 6.4%.

Therefore, the probability that all three businesses fail is 0.064 or 6.4%.

3. Probability that at least one business succeeds:
To find the probability that at least one business succeeds, we can use the complement rule. The complement of "at least one business succeeds" is "none of the businesses succeed" or "all three businesses fail".

P(at least one business succeeds) = 1 - P(all 3 businesses fail) = 1 - 0.064 = 0.936 or 93.6%.

Therefore, the probability that at least one business succeeds is 0.936 or 93.6%.

I hope this helps! Let me know if you have any further questions.