twenty light bulbs are tested to see if they claims last long as the manufacturers claims they do. three light bulbs failed the test. two light bulbs are selected at random without replacement from this collection of bulbs find the probability that both light bulbs failed the test. round your answer to the to three decimal places

prob = (3/20)(2/19) = 3/190

same question as:

I have 20 marbles of which 3 are red
I choose 2 without replacement, what is the probability that they are both red

Well, light bulbs failing the test is definitely not a bright idea! But let's calculate the probability for you.

Out of the 20 tested bulbs, 3 failed the test. This means we have 17 bulbs left that passed the test.

When you select the first bulb, you have a 3/20 chance of picking a failed bulb.

After that, there are 19 bulbs left, with 2 of them being failed bulbs. So when you pick the second bulb, you have a 2/19 chance of selecting another failed bulb.

To find the probability of both events occurring, you simply multiply the individual probabilities together. So the probability is:

(3/20) * (2/19) = 0.01578947368

Rounded to three decimal places, the probability is approximately 0.016.

So, the probability that both light bulbs failed the test is roughly 0.016. It seems Lady Luck wasn't shining so brightly on those bulbs!

To find the probability that both light bulbs failed the test, we need to calculate the probability of selecting a failed bulb on the first draw and a failed bulb on the second draw without replacement.

There are a total of 20 light bulbs, and 3 of them failed the test. Therefore, the probability of selecting a failed bulb on the first draw is 3/20.

After the first light bulb is selected and not replaced, there are 19 light bulbs remaining, and 2 failed bulbs. Therefore, the probability of selecting a failed bulb on the second draw is 2/19.

To find the probability of both events occurring, we multiply the probability of the first event by the probability of the second event:

P(both bulbs failed) = (3/20) * (2/19) = 6/380 = 3/190 = 0.0158 (rounded to three decimal places).

Therefore, the probability that both light bulbs failed the test is approximately 0.0158.

To find the probability that both light bulbs failed the test, we need to determine the probability of selecting a failed light bulb on the first draw and then selecting another failed light bulb on the second draw without replacement.

Let's calculate the probability step by step:

Step 1: Determine the probability of selecting a failed light bulb on the first draw.
Since three bulbs failed the test out of a total of twenty bulbs, the probability of selecting a failed light bulb on the first draw is 3/20.

Step 2: Determine the probability of selecting another failed light bulb on the second draw without replacement.
After the first bulb is selected, there are now 19 bulbs remaining, with two failed bulbs among them. So, the probability of selecting another failed light bulb on the second draw is 2/19.

Step 3: Multiply the probabilities calculated in steps 1 and 2.
To find the probability of both events happening (selecting a failed light bulb on the first draw and then another failed light bulb on the second draw), we need to multiply the probabilities from steps 1 and 2:

(3/20) * (2/19) = 6/380 = 0.01579.

Therefore, the probability that both light bulbs selected at random without replacement failed the test is approximately 0.016 (rounded to three decimal places).