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An ordinary (fair) die is a cube with numbers 1 through 6 on the sides. Imagine that such a die is rolled twice in succession and that the face values of the two rolls sre added together. The sum is recorded as the outcome of a single trial of a random experiment. Compute the probability of each of the following events. Event A: The sum is greater than 5. Event B: The sum is an odd number. P(A)= P(B)=

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The sample space of rolling two dice has 36 possible outcomes. Remember that the "sample space" is a set which contains all possible outcomes.

(1,1) (2,1) (3,1) (4,1) (5,1) (6,1)

(1,2) (2,2) (3,2) (4,2) (5,2) (6,2)

(1,3) (2,3) (3,3) (4,3) (5,3) (6,3)

(1,4) (2,4) (3,4) (4,4) (5,4) (6,4)

(1,5) (2,5) (3,5) (4,5) (5,5) (6,5)

(1,6) (2,6) (3,6) (4,6) (5,6) (6,6)

The probability of rolling a 2 is 1/36.

The probability of rolling a 3 is 2/36.

The probability of rolling a 4 is 3/36.

The probability of rolling a 5 is 4/36.

The probability of rolling a 6 is 5/36.

The probability of rolling a 7 is 6/36.

The probability of rolling an 8 is 5/36.

The probability of rolling a 9 is 4/36.

The probability of rolling a 10 is 3/36.

The probability of rolling an 11 is 2/36.

The probability of rolling a 12 is 1/36.

Event A: The sum is greater than 5.

Probability of rolling a number bigger than 5 is the sum of the probabilities of rolling a 6, 7, 8, 9, 10, 11, and 12.

5/36 + 6/36 + 5/36 + 4/36 + 3/36 + 2/36 + 1/36 = 26/36 which reduces to 13/18

Event B: The sum is an odd

The probability that the sum is odd is 50%.

Sum = 3, 5, 7, 9, 11

P(B) = 18/36 = 50%

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