A certain type of new business succeeds 60% of the time. Suppose that 3 such businesses open (where they do not compete with each other, so it is reasonable to believe that their relative successes would be independent). Which of the following distributions would you use to figure out the probability that all of them will fail?
A) binomial distribution
B) uniform distribution
C) Poisson distribution
D) normal distribution

Question

Quizplus · Accepted Answer

The binomial distribution is used when there are a fixed number of independent trials, each with only two possible outcomes (success or failure), and the probability of success is constant across all trials. In this case, we have three independent trials (the opening of three businesses), each with a probability of success of 0.6 and a probability of failure of 0.4. Therefore, we can use the binomial distribution to calculate the probability that all three businesses will fail.

A Certain Type of New Business Succeeds 60% of the Time