Answer:
0.691
Explanation:
The probability of 2 or fewer of the 10 business ideas being successful can be calculated using the binomial probability formula, which is:
P(X) = (n choose x) * p^x * (1-p)^(n-x)
In this formula, n is the total number of trials (in this case, the number of business ideas), x is the number of successful outcomes (in this case, the number of successful business ideas), p is the probability of success for each trial, and (n choose x) is the binomial coefficient, which represents the number of ways that x successes can occur in n trials.
Plugging in the values from the problem, we can calculate the probability of 2 or fewer successful business ideas as follows:
P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)
P(X = 0) = (10 choose 0) * (0.442)^0 * (0.558)^10 = 0.060
P(X = 1) = (10 choose 1) * (0.442)^1 * (0.558)^9 = 0.285
P(X = 2) = (10 choose 2) * (0.442)^2 * (0.558)^8 = 0.346
Adding these probabilities together, we get:
P(X ≤ 2) = 0.060 + 0.285 + 0.346 = 0.691
Thus, the probability that 2 or fewer of the 10 business ideas will be successful is approximately 0.691.