Simon wants to earn as many points as possible in one turn in a game. Two number cubes whose sides are numbered 1 through 6 are rolled. He is given two options for the manner in which points are awarded in the turn.

OPTION A: If the sum of the rolls is a prime number, Simon receives 15 points.
OPTION B: If the sum of the rolls is a multiple of 3, Simon receives 12 points.

Which statement best explains the option he should choose?

A. Simon should choose Option B. The mathematical expectation of this option is 6.25 and is the greater mathematical expectation of the two options.

B. Simon should choose Option A. The mathematical expectation of this option is 6.25 and is the greater mathematical expectation of the two options.

C. Simon should choose Option B. The mathematical expectation of this option is 4 and is the greater mathematical expectation of the two options.

D. Simon should choose Option A. The mathematical expectation of this option is 4 and is the greater mathematical expectation of the two options.

Answer: b. Simon should chose option a. The mathematical expectation of this option is 6.25 and is the greater mathematical expectation of the two options.

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maheshpatelvVT maheshpatelvVT · Answer 2 · 2022-05-25T10:54:55+02:00

Statement B. Simon should choose Option A. The mathematical expectation of this option is 6.25 and is the greater mathematical expectation of the two options is correct.

What is probability?

It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

The probability that the sum of the rolls is a prime number:

P(sum is prime) = 15/36 =0.416

Expected number of points = 0.416×15 =6.25

Probability that f the sum of the rolls is a multiple of 3,

P(sum of rolls is multiple of 3) = 12/36 = 0.33

Expected number of points = 0.33×12 = 3.96

Thus, statement B. Simon should choose Option A. The mathematical expectation of this option is 6.25 and is the greater mathematical expectation of the two options is correct.

Learn more about the probability here:

brainly.com/question/11234923

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