For the experiment of tossing a six sided die twice, what is the probability that...

Jovany Clayton

Jovany Clayton

Answered

2022-07-07

For the experiment of tossing a six sided die twice, what is the probability that the sum is less than 11?

Answer & Explanation

Dalton Lester

Dalton Lester

Expert

2022-07-08Added 12 answers

Step 1
Without loss of generality we could assume that one die is red and the other is green
For each of the 6 red outcomes there are 6 green outcomes.
This means that there are a combined collection of 6 × 6 = 36 possible outcomes.
Step 2
Of the 36 possible outcomes only 3 result in totals greater than on equal to 11; namely XXX < red , green > { < 5 , 6 > , < 6 , 5 > , < 6 , 6 > }
Therefore, there are 36 - 3 = 33 possible outcomes for which the sum is less than 11.
Since each outcome is (assumed to be) equally probable, XXX P ( sum < 11 ) = 33 36 = 11 12

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