Question

your company has an agreement according to which it can return to the supplier shipments where 3+ containers have faulty materials). According to the same agreement, your company is entitled to compensation on a progressive scale. Specifically, a clause in the agreement states that the supplier will compensate your company as follow: If more than 4 but less than 7 containers are faulty, the supplier will pay a penalty of $10,000; If there are 7 or more faulty containers but less than 10 then the penalty would increase to $15,000, and; if at least 10 are faulty the supplier pays a penalty of $20,000.

(1) What are the chances that the supplier will have to pay a penalty?

(2) What are the chances that the supplier will not have to pay a penalty?

(3) What is the probability that the supplier will have to pay at most $15,000?

(4) What is the likelihood that the supplier will have to pay $15,000 or more?

Hint 1: When working with complex events it is important to pay close attention to the following keywords: lass than, more than, X or more, X or less, no more than, no less than, at most, and at least.

Hint 2: Create a new random variable, PenaltyPaidBySupplier. List the possible outcomes and specify their probabilities

Number of faulty containers	Frequency
0	93
1	7
2	5
3	4
4	2
5	1
6	1
7	1
8	2
9	1
10 or more	3

Answer 1

1.

P(penalty) = sum of freq ((no. of faulty conatiner) > 4) / total freq.

= 9/120 = 3/40 = 0.075

P(penalty) = 0.075

2.

P(no penalty) = sum of freq ((no. of faulty conatiner) <= 4) / total freq.

= 111/120 = 0.925

3.

P(penalty<=15000$) = sum of freq ((no. of faulty conatiner) <10) / total freq.

= 117/120 = 39/40 = 0.975

4.

P(penalty >= 15000$) = sum of freq ((no. of faulty conatiner) >= 7) / total freq.

= 7/120 = 0.05833

P.S. (please upvote if you find the answer satisfactory)