Question

find the indicated probability.
a local factory uses a manufacturing process in which 70% of the final products meet quality standards and 30% are found to be defective. if three of the products are randomly selected, find the probability that all of them are acceptable.
(1 point)
○ 0.027
○ 0.343
○ 0.429
○ 2.1

Explanation:

Step1: Identify the probability of one product being acceptable

The probability that a single product meets quality standards is \(p = 0.7\)

Step2: Use the multiplication rule for independent events

Since the selections are independent, the probability that all three are acceptable is \(P=\underbrace{0.7\times0.7\times0.7}_{n = 3\text{ times}}\)

$$P=(0.7)^3=0.343$$

Answer:

0.343