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Your friend says she has an unfair die: the probability of getting a one or a six is 1/3 for each, and the probability of getting a two, three, four, or five is 1/12 for each.

You want to test her statement. If you roll the die 96 times, what are the expected values for each number on the die?

A. The expected values are 8 for both ones and sixes, and 32 for twos, threes, fours and fives.

B. The expected values are 32 for both ones and sixes, and 8 for twos, threes, fours and fives.

C. The expected values are 8 for ones, twos, and threes, and 32 for fours, fives and sixes.

D. All categories have the same expected value of 16.

E. All categories have the same expected value of 32.

Respuesta :

Answer:

B. The expected values are 32 for both ones and sixes, and 8 for twos, threes, fours and fives.

Step-by-step explanation:

Probability is a likely hood of an event happening in the statement the probability of getting 1 or 6 after rolling the die is 4 times more than getting the other 4 numbers i.e. 2,3,4, 5  

Total roll of die 96  

Expected outcome from the roll

Probability of getting #1 = 1/3 = 4/12      ∴96 x 4/12 = 32

Probability of getting #2 = 1/12     ∴96 x 1/12 = 8

Probability of getting #3 = 1/12      ∴96 x 1/12 = 8

Probability of getting #4 = 1/12          ∴96 x 1/12 = 8

Probability of getting #5 = 1/12   ∴ 96 x 1/12 = 8

Probability of getting #6 = 1/3 = 4/12  ∴96 x 4/12 = 32

The expected values are 32 for both ones and sixes, and 8 for twos, threes, fours and fives.

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