MathematicsA pair of dice is thrown once. What is the probability that 5 will come up at least on one die?

A pair of dice is thrown once. What is the probability that 5 will come up at least on one die?


  1. A
    1336
  2. B
    536
  3. C
    136
  4. D
    1136 

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    Solution:

    Given that a pair of dice is thrown once.
    We know that the probability is given as the ratio of the number of favorable outcomes with the total number of possible outcomes.
    P(E)=Number of favourable outcomes n(E)Total possible outcomes n(S)
    There are 36 possible outcomes when two dies are thrown, 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 5 will occur at least one die.
    Favourable outcomes are:
    E={(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(1,5),(2,5),(3,5),(4,5),(6,5)} n(E)=11
    The probability of getting 5 on at least one die is,
    P(E)=Number of favourable outcomes n(E)Total number of outcomes n(S)
    P(E)=1136 Therefore, the probability of getting 5 on at least one die is 1136.
    Hence, option 4 is correct.
     
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