Final answer:
The probability that a container with 2 defective diesel engines will be shipped when 8 engines are chosen at random is 1/45, calculated using combinations in Mathematics.
Step-by-step explanation:
The subject of this question is Mathematics, specifically involving probability and combinatorics. A container has 10 diesel engines, with 2 being defective. The company will only ship the container if none of the randomly selected 8 engines are defective. The probability that the container is shipped can be found by considering the number of ways to choose 8 engines that are not defective out of the 10 engines, relative to the total number of ways to choose 8 engines out of 10 without any restrictions. Since there are 2 defective engines, there are 8 non-defective engines in total.
To calculate this, we use combinations: The number of ways to choose 8 non-defective engines from the 8 available is given by 8 choose 8 (which is 1 way), while the total number of ways to choose any 8 engines from the 10 is given by 10 choose 8. The probability is the ratio of these two numbers.
Using the combination formula which is n choose k = n! / (k!(n - k)!), we can calculate:
- 8 choose 8 = 1 (since 0! = 1 by definition)
- 10 choose 8 = 10! / (8!(10 - 8)!) = 45
The probability is therefore 1/45. Hence, the probability that a container will be shipped, even though it contains 2 defective engines, when 8 engines are chosen at random is 1/45.