MathematicsTwo dice are thrown at the same time. Find the probability that the sum of the two numbers appearing on the top of the dice is more than 10 .

Two dice are thrown at the same time. Find the probability that the sum of the two numbers appearing on the top of the dice is more than 10 .


  1. A
    1112
  2. B
    712
  3. C
    512
  4. D
    112 

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    Solution:

    Given that the two dice are thrown at the same time.
    Therefore there are 36 possible outcomes.
    The outcomes are,
    {(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),
    (3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3)(4,4)(4,5),(4,6),
    (51),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4)(6,5)(6,6)}
     Total possible outcomes, n(S)=36.
    Let E be the event that numbers occurring on top are having the sum as 10 or more than that.
    Favourable outcomes are 5,6 , 6,5 , 6,6   .   Total number of favourable outcomes, n(E)=3
    Probability of event E is,
    P(E)=Number of favourable outcomes n(E)Total number of outcomes n(S)
    P(E)=336
    P(E)=112
    Therefore, the probability of getting two numbers on top whose sum is 10 or more than that is 112.
    Hence, option 4 is correct.
     
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