Probability


  1. Two dice are thrown simultaneously. What is the probability of getting a number other than 4 on any dice ?









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    Here, n(S) = 6 x 6 = 36 and E = Event of getting a number other than 4 on any dice
    = {(1, 1), (1, 2), (1, 3), (1, 5), (1, 6), (2, 1), (2, 2) , (2, 3) , (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 5), (3, 6), (5, 1) , (5, 2) , (5, 3), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 5), (6, 6) }

    Correct Option: A

    Here, n(S) = 6 x 6 = 36 and E = Event of getting a number other than 4 on any dice
    = {(1, 1), (1, 2), (1, 3), (1, 5), (1, 6), (2, 1), (2, 2) , (2, 3) , (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 5), (3, 6), (5, 1) , (5, 2) , (5, 3), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 5), (6, 6) }
    ∴ P(E) = n(E) / n(S) = 25/36


  1. Number 1 to 25 are marked on tokens of equals size one on each. A token is drawn at random. Find the probability of getting a number divisible by both 2 and 3?









  1. View Hint View Answer Discuss in Forum

    Total number of ways of selecting one number from 25 number is 25C1 ways.
    Let E be the event of drawing a number divisible by both 2 and 3
    i.e., (if a number is divisible by both 2 and 3, it is divisible by 6 also)

    Correct Option: A

    Total number of ways of selecting one number from 25 number is 25C1 ways.
    Let E be the event of drawing a number divisible by both 2 and 3
    i.e., (if a number is divisible by both 2 and 3, it is divisible by 6 also)
    E = {6, 12, 18, 24}
    ∴ Required probability = P(E) = n(E) / n(S) = 4/25



  1. A complete cycle of a traffic light takes 60 s. During each cycle the light is green for 25 s, yellow for 5 s and red for 30 s. At a randomly chosen time, the probability that the light will not be green is ?









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    Probability that light will be green = (Time for which light is green)/(time taken for complete cycle)

    Correct Option: D

    Time taken for complete cycle = 60 s
    Probability that light will be green = (Time for which light is green)/(time taken for complete cycle)
    = 25/60 = 5/12
    ∴ Probability that light will not be green = 1- 5/12 = 7/12


  1. The probability that a man will live 10 more year is 1/4 and the probability that his wife will live 10 more year is 1/3. Then, the probability that none of them will be alive after 10 yr, is ?









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    Let the name of the man be A and that of his wife be B. Then ,P(A will not be alive after 10 yr and B will not be alive after 10yr) = 3/4 x 2/3 = 1/2

    Correct Option: B

    Let the name of the man be A and that of his wife be B. Then ,P(A will not be alive after 10 yr and B will not be alive after 10yr) = 3/4 x 2/3 = 1/2



  1. The letters B, G, I, N, R are rearranged to form the word 'BRING'. Find its probability ?









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    The five letters could be arrange in 5! ways.
    One of them is 'BRING'.

    Correct Option: A

    The five letters could be arrange in 5! ways.
    One of them is 'BRING'.
    ∴ Required probability = 1/5!
    = 1/(5 x 4 x 3 x 2 x 1)
    = 1/120