- 1 Marks
Question
A large batch of components of TV sets is stocked by a company. The batch comprises components that are manufactured by processes A, B, and C. There are twice as many components from process A as from each of processes B and C in a batch. Components from A contain 8% defectives, and those from B and C contain 11% and 14% defectives respectively.
The probability that a defective item is from process B is:
A. 0.228
B. 0.238
C. 0.248
D. 0.258
E. 0.268
Answer
Answer: E. 0.268
Explanation:
Let the number of components from process B be denoted as x. The number of components from A is 2x, and the number from C is also . The total number of components is 4x. The total defective rate for the batch is calculated by finding the weighted sum of the defective rates from each process:
Now, to find the probability that a defective component came from process B, we use:
Thus, the correct probability is 0.268, corresponding to option E.
- Tags: Business Mathematics, Defective Items, Probability
- Level: Level 1
- Topic: Statistics
- Series: MAY 2017
- Uploader: Kwame Aikins