Q4.A retailer of wrist watches before accepting a lot of 50 watches tests at random 5 watches andif they are all right, accepts the lot. Find the probability that a lot containing 3 defectives isaccepted by him.
Question
Q4.A retailer of wrist watches before accepting a lot of 50 watches tests at random 5 watches andif they are all right, accepts the lot. Find the probability that a lot containing 3 defectives isaccepted by him.
Solution
The problem can be solved using the concept of combinations in probability.
Step 1: Identify the total number of watches and the number of defective watches. In this case, there are 50 watches in total and 3 of them are defective.
Step 2: The retailer tests 5 watches at random. We need to find the probability that all 5 watches are non-defective.
Step 3: The number of ways to choose 5 watches out of 50 is given by the combination 50C5.
Step 4: The number of ways to choose 5 non-defective watches out of 47 (since 3 are defective) is given by the combination 47C5.
Step 5: The probability that a lot containing 3 defectives is accepted by him is given by the ratio of the number of favorable outcomes to the total number of outcomes.
So, the probability P = 47C5 / 50C5.
Step 6: Calculate the values. 47C5 = 1,533,939 and 50C5 = 2,118,760.
Step 7: Substitute the values into the formula. P = 1,533,939 / 2,118,760 = 0.7236 (rounded to four decimal places).
So, the probability that a lot containing 3 defectives is accepted by the retailer is approximately 0.7236 or 72.36%.
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