A large disaster cleaning company estimates that each of the jobs it bids on are finished within the bid time with probability 0.3 independent of each other job it bids on. Consider a random sample of 8 jobs that is has contracted.
-What is the probability that exactly 4 of the jobs were not completed within the bid time?
A)0472
B)1361
C)2293
D)3471
E)4441

Question

Quizplus · Accepted Answer

We can use the binomial probability formula: 
P(X=k) = nCk * p^k * (1-p)^(n-k)
where n is the number of trials, k is the number of successes, p is the probability of success, and (1-p) is the probability of failure.

In this case, n = 7, k = 4, p = 0.3 (since 30% of the jobs were not completed within the bid time), and (1-p) = 0.7.

Substituting these values into the formula, we get:
P(X=4) = 7C4 * 0.3^4 * 0.7^3
P(X=4) = 35 * 0.0081 * 0.343
P(X=4) = 0.0975

Therefore, the probability that exactly 4 of the jobs were not completed within the bid time is 0.0975, which is closest to option B: 1361.

A Large Disaster Cleaning Company Estimates That Each of the Jobs