If you roll a pair of fair dice, what is the probability of each of the following? (round all answers to 4 decimal places, .XXXX
1 answer:
Answer: The required probabilities are
Step-by-step explanation: Given that a pair of fair dice is rolled.
We are to find the probability of getting
(a) getting a sum of 1.
b) getting a sum of 5.
c) getting a sum of 12.
Let S be the sample space for the experiment of rolling a pair of fair dice.
Then, S = {(1,1), (1,2), (1,3), (1, 4), (1,5), (1,6), . . . , (6,5), (6,6)}.
And, n(S) =36.
(a) Let E denote the event of getting a sum of 1.
Since the sum of the numbers on two dice is minimum 2, so
E = { } ⇒ n(E) = 0.
Therefore, the probability of event E is
(b) Let F denote the event of getting a sum of 5.
Then,
F = {(1,4), (2,3), (3,2), (4,1)} ⇒ n(F) = 4.
Therefore, the probability of event F is
(c) Let G denote the event of getting a sum of 12.
Then,
G = {(6,6)} ⇒ n(G) = 1.
Therefore, the probability of event G is
Thus, the required probabilities are
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