Question

A bag contains 11 numbered chips inside. Two chips are labeled 1, three are labelled 2, and six are labelled 3. Let the random variable X = "number on a chip in the bag."
What is the expected number of a chip that is randomly chosen from the bag?

Answer 1

Well, what chip has the most quantity?

Answer 2

if you only have 2 1's and you have 3 2's, which one are you most likely to pull?

Answer 3

2s?

Answer 4

yea

Answer 5

so if you have 3 2's and 6 3's, which one?

Answer 6

6 3s?

Answer 7

lol I'm so confusedddddddddd! XD

Answer 8

yes

Answer 9

so there are more 3's than any other number

Answer 10

therefore there is a higher probability of drawing one

Answer 11

lol I am still confused. I'm pretty sure there's more to it than that. lol irdk XD

Answer 12

expected value = \[\sum_{}^{}x*P(x)\]

where x is the value of an event, and P(x) is the probability of that event. the sigma sign means that we sum across all events.

Answer 13

put more simply, you'd multiply (the value of a chip) * (the probability of getting that value), repeat with all values, and sum the result

start with: "Two chips are labeled 1"

the value is 1
the probability is 2/11 since there are 11 chips

so for this x-value, you'd multiply (1)*(2/11)

repeat with the other values, and sum the results

Answer 14

Thank you so much!