Question

A container holds 50 electronic components, of which 10 are defective. If 6 components are drawn at random from the container, what is the probability that at least 4 of them are not defective?

1) 0.26
2) 0.42
3) 0.75
4) 0.91
5) 1

Answer 1

To calculate the probability that at least 4 out of 6 components drawn are not defective, we need to find the individual probabilities of drawing exactly 4, 5, and 6 non-defective components and add them together. The probability is approximately 0.5329.

Step-by-step explanation:

To find the probability that at least 4 out of 6 components drawn are not defective, we need to calculate the probability of getting 4, 5, or 6 components that are not defective and add them together.

First, let's calculate the probability of drawing exactly 4 components that are not defective. There are 40 non-defective components and 10 defective components, so the probability of drawing 4 non-defective components is:

P(4 non-defective components) = (40/50) * (39/49) * (38/48) * (37/47) * (10/46) * (9/45) ≈ 0.2555

Similarly, the probability of drawing exactly 5 non-defective components is:

P(5 non-defective components) = (40/50) * (39/49) * (38/48) * (37/47) * (36/46) * (10/45) ≈ 0.1885

And the probability of drawing exactly 6 non-defective components is:

P(6 non-defective components) = (40/50) * (39/49) * (38/48) * (37/47) * (36/46) * (35/45) ≈ 0.0889

Now, we can add these probabilities together to get the probability of at least 4 non-defective components:

P(at least 4 non-defective components) = P(4 non-defective components) + P(5 non-defective components) + P(6 non-defective components) ≈ 0.2555 + 0.1885 + 0.0889 ≈ 0.5329

So the probability that at least 4 out of 6 components drawn are not defective is approximately 0.5329.