Question

Find the probability that the sum is as stated when a pair of dice is rolled. (Enter your answers as fractions.)
(a) odd and doubles


(b) odd or doubles

Answer 1

Answer on Question #66364 – Math – Statistics and Probability

Question

Find the probability that the sum is as stated when a pair of dice is rolled. (Enter your answers as fractions.)

(a) odd and doubles

(b) odd or doubles

Solution

Total number of outcomes:

$$N = 6 * 6 = 36,$$

because scores on the dice are independent.

Odd sums: (1,6), (1,4), (1,2), (2,5), (2,3), (2,1), (3,6), (3,4), (3,2), (4,5),

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

There are 18 pairs.

Doubles: (1,1), (2,2), (3,3), (4,4), (5,5), (6,6).

There are 6 pairs.

(a) $P(\text{odd and doubles}) = 0$.

(b) $P(\text{odd or doubles}) = \frac{18 + 6}{36} = \frac{24}{36} = \frac{2}{3}$.

Answer: (a) 0; (b) 2/3.

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