A warehouse contains six parts made by company A and ten parts made by company B. If four parts are selected at random from the warehouse, the probability that none of the four parts is from company A is approximately 0.1154.

Question

Quizplus · Accepted Answer

Let's use the formula for probability of an event:
P(event) = (number of successful outcomes) / (total number of outcomes)

In this case, the "successful outcomes" are selecting four parts from company B, and the "total number of outcomes" is selecting any four parts from the warehouse. We can use combinations to calculate these numbers:

- Number of ways to choose 4 parts from company B: C(10,4) = 210
- Number of ways to choose any 4 parts from the warehouse: C(16,4) = 1820

So the probability of selecting 4 parts from company B is:
P(BBBB) = 210 / 1820 = 21 / 182

To check the given probability of approximately 0.1154, we can use a calculator or software to find the closest value of P(BBBB) that matches:

- P(BBBB) ≈ 0.115372

This is very close to the given probability, so we can say that the statement is true: the probability of selecting four parts at random from the warehouse and getting none from company A is approximately 0.1154.

A Warehouse Contains Six Parts Made by Company a and Ten