Question

The grams of sugar per serving for three brands of cereal are 4 g, 10 g, and 14 g. The probability of choosing a cereal with 4 grams of sugar is 1/4 . The probability of choosing a cereal with 10 grams of sugar is 5/8 . The probability of choosing a cereal with 14 grams of sugar is 1/8 .

What is the expected value of the number of grams of sugar in cereal?

Answer 1

`Expected\ Value = 9`

Explanation:

Given

Cereal A

`Probability = (1)/(4)`

`Grams = 4`

Cereal B

`Probability = (5)/(8)`

`Grams = 10`

Cereal C

`Probability = (1)/(8)`

`Grams = 14`

Required

Determine the expected value of grams of sugar

This is calculated by multiplying the probability and grams of sugar in each cereal.

The results of the products are then added together

i.e.

`Expected\ Value = (1)/(4) * 4 + (5)/(8) * 10 + (1)/(8) * 14`

`Expected\ Value = 1 + (50)/(8)+ (14)/(8)`

`Expected\ Value = 1 + 6.25 + 1.75`

`Expected\ Value = 9`

Hence;

The expected value of grams of sugar is 9 grams