4 calculators were selected at random from a sample of 44 calculators that were defective and 22 that were in good condition. Find the probability that all 4 calculators are defective.
Ok, I'll just start this one. There are
66 choose 4 samples. yes/no?
What is the P of 0,1,2,3,4 defecives in a sample? You need to caluclate these. I wouldn't be surprised if there's a sample or formula for this problem in your text. Look there first.
Looks like my observation skills are sliding. You only want to know the P that all of them are defects. So I don't think you should need to do as much calculating as I thought.
To find the probability that all 4 calculators selected are defective, we need to calculate the probability of selecting a defective calculator from the total pool of calculators.
Let's start by calculating the probability of selecting a defective calculator from the sample.
There are 44 defective calculators out of a total of 44 defective calculators and 22 good calculators. Therefore, the probability of selecting a defective calculator is:
P(defective) = (number of defective calculators) / (total number of calculators)
= 44 / (44 + 22)
= 44 / 66
= 2/3
Now, since the selection of calculators is done randomly and independently, we can multiply the probabilities together:
P(all 4 defective) = P(defective) * P(defective) * P(defective) * P(defective)
= (2/3) * (2/3) * (2/3) * (2/3)
= (2/3)^4
≈ 0.1975 or 19.75%
Therefore, the probability that all 4 calculators selected are defective is approximately 0.1975 or 19.75%.