A regular six-sided die, with sides numbered 1 through 6, is rolled three times. What is the probability that the sum of the three rolls is at least 4? 2 Mark For ReviewA) B) C) D)
Question
A regular six-sided die, with sides numbered 1 through 6, is rolled three times. What is the probability that the sum of the three rolls is at least 4? 2 Mark For ReviewA) B) C) D)
Solution
To solve this problem, we first need to understand the total number of outcomes when a die is rolled three times. Since a die has 6 faces, the total number of outcomes is 666 = 216.
Next, we need to find out the number of outcomes where the sum of the three rolls is less than 4. The only possibilities are (1,1,1), (1,1,2), (1,2,1), (2,1,1). So, there are 4 such outcomes.
The probability that the sum of the three rolls is less than 4 is therefore 4/216 = 1/54.
Since we want the probability that the sum is at least 4, we subtract this from 1 (since the total probability of all outcomes is 1). So, the probability that the sum of the three rolls is at least 4 is 1 - 1/54 = 53/54.
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