Question

Juan counted all the beads in each necklace at the jewelry store where he works. Number of beads Number of necklaces 57 3 65 4 74 3 98 2 151 5 171 3 X is the number of beads that a randomly chosen necklace had. What is the expected value of X? Write your answer as a decimal.

Answer 1

The expected value is the sum of: [(each of the possible outcomes) × (the probability of the outcome occurring)].

The total number of necklaces is:

3 + 4 + 3 + 2 + 5 + 3 = 20 necklaces

Possible outcomes are 57 beads, 65 beads, 74 beads, 98 beads, 151 beads, and 171 beads.

The probabilities of each of the possibilities are:

57 beads = 3/20

65 beads = 4/20

74 beads = 3/20

98 beads = 2/20

151 beads = 5/20

171 beads = 3/20

Now, we substite into the expected value formula: