10th Class Mathematics Probability Question Bank Probability

  • question_answer A black die, a red die and a green die are thrown at the same time. What is the probability that the sum of three numbers that turn up is 15?

    A)  \[\frac{11}{216}\]                 

    B)  \[\frac{5}{108}\]                   

    C)  \[\frac{9}{216}\]                   

    D)  \[12\frac{1}{18}\]                 

    Correct Answer: B

    Solution :

    Total number of outcomes when three dice are thrown \[=6\times 6\times 6=216\] For sum of numbers to be 15, possible ways are, (6, 6, 3). (6, 3, 6), (3, 6, 6), (6, 5, 4), (6, 4, 5), (5, 4, 6), (5, 6, 4), (4, 5, 6), (4, 6, 5), (5, 5, 5) \[\therefore \] Number of favorable outcomes =10 \[\therefore \] Required probability \[=\frac{10}{216}=\frac{5}{108}\]

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