Question

Dave has just left an interview with a prospective employer. The hiring manager told Dave that she will tolerate one mistake during his first year but will fire him if he makes two mistakes. Based on Dave’s research and understanding of the job, he estimates that he will have to make five critical decisions during the year, and with his knowledge of the processes, figures that he will have about an 80% chance of making any of those five decisions correctly. Dave does not want to run any more than a 25% chance of being fired. If each of the decisions is independent of the others, should Dave risk taking the job if offered?

Answer 1

Let the random variable X = number of mistake during five critical decisions during the year,

X will have a binomial distribution with parameter n and p. The distribution can be represented as;

Now, the probability that Dave make at most one mistake is,

The probability of making more than one mistake = 1 - 0.73728 = 0.2627.

Since the chance of making more than one mistake is 26.27% which is greater than 25% hence Dave should not take the jbo offered.