Question
When two dice are rolled, what is the probability that the sum is either 7 or 11?
When two dice are rolled, what is the probability that the sum is either 7 or 11?
Answer: Option D
(5, 6), (6, 5)
=> Number of ways in which we get a sum of 11 = 2
P(a sum of 7 or a sum of 11) = P(a sum of 7) + P( a sum of 11)
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Answer : Option D
Explanation :
Total number of outcomes possible when a die is rolled = 6 (∵ any one face out of the 6 faces)
Hence, total number of outcomes possible when two dice are rolled = 6 × 6 = 36
To get a sum of 7, the following are the favourable cases.
(1, 6), (2, 5), {3, 4}, (4, 3), (5, 2), (6,1)
=> Number of ways in which we get a sum of 7 = 6
$MF#%\text{P(a sum of 7) = }\dfrac{\text{Number of ways in which we get a sum of 7}}{\text{Total number of outcomes possible}} = \dfrac{6}{36}$MF#%
To get a sum of 11, the following are the favourable cases.(5, 6), (6, 5)
=> Number of ways in which we get a sum of 11 = 2
$MF#%\text{P(a sum of 11) = }\dfrac{\text{Number of ways in which we get a sum of 11}}{\text{Total number of outcomes possible}}=\dfrac{2}{36} $MF#%
Here, clearly the events are , we haveP(a sum of 7 or a sum of 11) = P(a sum of 7) + P( a sum of 11)
$MF#%= \dfrac{6}{36} + \dfrac{2}{36} = \dfrac{8}{36} = \dfrac{2}{9}$MF#%
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