Question

A corporate trainer is teaching loan officers to identify risky borrowers from the available information they have on hand. The trainer has noticed over time that the trainee's ability to correctly identify borrowers as a risky or does not seem to change (at least in the short run, say, under 20 trials) over the trials nor is it influenced by whether the loan officer got the previous prediction correct. On average, stufents identify borrows correctly 65% of the time.

During a training exercise, the trainer was interested in the chance that a trainee loan officer would get 2 or more identifications correct out of 4 attempts.

1. Determine the probability that a trainee will get exactly 2 identifications correct

2. Determine the probability that a trainee will get 2 or more identifications correct

Answer 1

given that

p=Probability that , students identify borrows correctly =0.65

let X is number of time student identify borrows correctly out of 4 attempts

so

X~Bin (4,0.65)

so

1.

we have to find P(X=2)

now

2)

we have to find P(X>2)

now