If 3 dices are rolled, what is the probability of getting sum of the values on them is 11?Question 18Answera.31/216b.9/216c.27/216d.13/216
Question
If 3 dices are rolled, what is the probability of getting sum of the values on them is 11?
Question 18
Answer
- a. 31/216
- b. 9/216
- c. 27/216
- d. 13/216
Solution
To solve this problem, we need to find all the possible outcomes that sum up to 11 when three dice are rolled.
- (2,3,6), (2,4,5), (2,5,4), (2,6,3), (3,2,6), (3,3,5), (3,4,4), (3,5,3), (3,6,2), (4,2,5), (4,3,4), (4,4,3), (4,5,2), (5,2,4), (5,3,3), (5,4,2), (6,2,3), (6,3,2)
- Each of these 18 outcomes can occur in 3! = 6 ways (since the three dice are distinct), so there are 18*6 = 108 successful outcomes.
The total number of outcomes when three dice are rolled is 6^3 = 216.
So, the probability of getting a sum of 11 when three dice are rolled is 108/216 = 0.5 or 1/2.
However, none of the options provided (a.31/216, b.9/216, c.27/216, d.13/216) match this result. There might be a mistake in the question or the provided options.
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