Question

Suppose there are 10 identical items. 10 items are selected one by one with replacement. What is the probability that a particular item is not selected?(round it to two decimal places As an exercise, consider number of items as 'n'. Find a general formula for probability. Especially, find out what happens when n becomes very large(You will use this concept later in a concept called Bagging)

Answer 1

Answer:

Step-by-step explanation:

Lets look at the first pick. There are 9 items that can be choosen, one that cannot. So the chance to not pick the one is 9/10.

All the other attempts are the same and have 9/10 chance. (as replacement happens)

Now these events are independent of eachother so the combined chance is

(9/10)^10

For the formula:

Number of items: n

One pick is: (n-1)/n

N pick together is [(n-1)/n]^n