If 20% of the bolts produced by a machine are defective, determine the probability that out of 4 bolts chosen at random, no defective bolt will be found.Group of answer choices10.500.40960.4050
Question
If 20% of the bolts produced by a machine are defective, determine the probability that out of 4 bolts chosen at random, no defective bolt will be found.Group of answer choices10.500.40960.4050
Solution
The problem is asking for the probability of not getting a defective bolt in 4 trials.
Step 1: Determine the probability of not getting a defective bolt in a single trial.
Since 20% of the bolts are defective, it means that 80% of the bolts are not defective. So, the probability of not getting a defective bolt in a single trial is 0.80 (or 80%).
Step 2: Determine the probability of not getting a defective bolt in 4 trials.
The probability of not getting a defective bolt in 4 trials is the product of the probabilities of not getting a defective bolt in each trial.
So, the probability of not getting a defective bolt in 4 trials is (0.80)^4 = 0.4096.
Therefore, the probability that out of 4 bolts chosen at random, no defective bolt will be found is 0.4096.
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