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The grams of sugar per serving for three brands of cereal are 4g,8g, and 16g. The probability of choosing a cereal with 4 grams of sugar is 1/4. The probability of choosing a cereal with 8 grams of sugar is 5/8. The probability of choosing a cereal with 16 grams of sugar is 1/8.

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

A 6

B 7

C 8

D 9

Verified Answer :

Answer: The expected value of the number of gram of the sugar in the cereal is 8 grams.

Step-by-step explanation:

When we multiply each of the possible outcomes by the likelihood each outcome will occur and find out the sum of the all values, we get the expected value of an experiment.

Here, the probability of the different brands 4g, 8g and 16g are 1/4, 5/8 and 1/8 respectively.

Thus, by the above definition,

The expected value of the number of grams of the sugar in the cereal = 4 g × its probability + 8 g × its possibility + 16 gram × Its possibility,

\(=4\times \frac{1}{4}+8\times \frac{5}{8}+16\times \frac{1}{8}\)

\(=1+5 +2 = 8\)

Thus, The expected value of the number of gram of the sugar in the cereal is 8 grams.

The expected value of the number of grams of sugar in cereal is 8 grams and this can be determined by using the given data.

Given :

  • The grams of sugar per serving for three brands of cereal are 4g, 8g, and 16g.
  • The probability of choosing a cereal with 4 grams of sugar is 1/4.
  • The probability of choosing a cereal with 8 grams of sugar is 5/8.
  • The probability of choosing a cereal with 16 grams of sugar is 1/8.

The following steps can be used in order to determine the expected value of the number of grams of the sugar in cereal:

Step 1 - The probability concept can be used in order to determine the expected value of the number of grams of sugar in the cereal.

Step 2 - According to the given data, the probability of choosing a cereal with 4 grams of sugar is 1/4, the probability of choosing a cereal with 8 grams of sugar is 5/8, and the probability of choosing a cereal with 16 grams of sugar is 1/8.

Step 3 - So, the expected value of the number of grams of the sugar in cereal is:

\(\rm Total \;number \;of\; grams\; of\; sugar=4\times \dfrac{1}{4}+8\times \dfrac{5}{8}+16\times \dfrac{1}{8}\)

Step 4 - Simplify the above expression.

Total number of grams of sugar = 8 grams

Therefore, the correct option is C).

For more information, refer to the link given below:

https://brainly.com/question/795909

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