Question

An employee at the craft store counted the number of red buttons in each bag of mixed buttons. Number of red buttons Number of bags 14 3 33 9 37 6 55 3 88 1 124 3 X is the number of red buttons that a randomly chosen bag had. What is the expected value of X? Write your answer as a decimal.

Answer 1

The basic expected value formula is the probability of an event multiplied by the number of times the event happens: (P(x) * n).

Step 1: we will have to get the probabilities of getting the red buttons

If P(A) is the probability of an event “A” n(A) is the number of favorable outcomes. n(S) is the total number of events in the sample space.

Then

`P\mleft(A\mright)\text{ =}(n(A))/(n(S))`

n(s) = total number of bags = 3 + 9 + 6 + 3 + 1 + 3 = 25

P(14 red bags) = 3/25 = 0.12

P(33 red bags) = 9/25 = 0.36

P(37 red bags) = 6/25 = 0.24

P(55 red bags) =3/25 = 0.12

P(88 red bags) = 1/25 = 0.04

P(124 red bags) = 3/25 = 0.12

Expected value = sum of all (Probabilities x number of red bags)

Expected values = (0.12 x 14 ) + (33x 0.36) + (37 x 0.24) + (55 x 0.12) + (88x 0.04) + (124 x 0.12)

=> 47.44

Expected value = 47.44