Expected ValueSuppose you go to a shoe shop to buy a pair of shoes. There are 50 pairs of shoes in the shop. Every time you ask the shopkeeper to show you a pair of shoes, he draws 3 pairs randomly from his stock of 50 pairs. If you do not like any of the pairs, he places all the 3 of them back and then draws 3 pairs again, randomly. Out of all the 50 pairs, 7 pairs of shoes are defective. What is the expected number of defective shoes in a given trial? Note: Round off your final answer to two decimal places. If your answer is 1.333333, write 1.33 in the box.
Question
Expected ValueSuppose you go to a shoe shop to buy a pair of shoes. There are 50 pairs of shoes in the shop. Every time you ask the shopkeeper to show you a pair of shoes, he draws 3 pairs randomly from his stock of 50 pairs. If you do not like any of the pairs, he places all the 3 of them back and then draws 3 pairs again, randomly. Out of all the 50 pairs, 7 pairs of shoes are defective. What is the expected number of defective shoes in a given trial? Note: Round off your final answer to two decimal places. If your answer is 1.333333, write 1.33 in the box.
Solution
To calculate the expected number of defective shoes in a given trial, we need to use the concept of expected value in probability.
The expected value is calculated by multiplying each possible outcome by the probability of that outcome, and then summing these values.
Step 1: Calculate the probability of drawing a defective pair of shoes. There are 7 defective pairs out of 50 total pairs, so the probability is 7/50 = 0.14.
Step 2: Calculate the expected value. In each trial, the shopkeeper draws 3 pairs of shoes. So, the expected number of defective shoes in a given trial is 3 * 0.14 = 0.42.
Therefore, the expected number of defective shoes in a given trial is approximately 0.42 when rounded to two decimal places.
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