A bag contains 8 items of which 2 are defective. A man selects 3 items at random. Find the expected number of defective items he has drawn.Group of answer choices0.750.57cant saynone of these
Question
A bag contains 8 items of which 2 are defective. A man selects 3 items at random. Find the expected number of defective items he has drawn.Group of answer choices0.750.57cant saynone of these
Solution
To solve this problem, we need to use the formula for the expected value of a random variable. The expected value is the sum of all possible outcomes, each multiplied by its probability.
Step 1: Identify the total number of items and the number of defective items. In this case, there are 8 items in total and 2 are defective.
Step 2: Identify the number of items the man selects. In this case, the man selects 3 items.
Step 3: Calculate the probability of drawing a defective item. The probability of drawing a defective item is the number of defective items divided by the total number of items. So, the probability is 2/8 = 0.25.
Step 4: Calculate the expected number of defective items. The expected number of defective items is the number of items the man selects multiplied by the probability of drawing a defective item. So, the expected number is 3 * 0.25 = 0.75.
So, the expected number of defective items the man has drawn is 0.75.
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