SOLUTION: Use the formula for the probability of the complement of an event. Two dice are tossed. What is the probability of getting a sum of at least 3? (Enter your probability as a frac

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Question 1132894: Use the formula for the probability of the complement of an event.
Two dice are tossed. What is the probability of getting a sum of at least 3? (Enter your probability as a fraction.)

Answer by ikleyn(52914) About Me  (Show Source):
You can put this solution on YOUR website!
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The full space of events is the set of all pairs (m,n), where m and n are integers between 1 and 6 inclusively 
- possible outcomes from each dice.


Thus the full space of events has 6*6 = 36 elements, each with the probability of 1%2F36.


The probability of getting the sum at least of 3 is the sum of probabilities of getting 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12 (maximum).


The complement event is to get the sum of 2, which is possible for only one configuration (m,n) = (1,1) of the base space of events.


So, the probability of getting this complement event is  1%2F36.


Hence, the probability that the problem asking for is  1+-+1%2F36 = 35%2F36.     ANSWER

The problem is solved.

Thus using the complement space of events, we are free from the need to analyse all 35 events of the base space.