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Home Aptitude Probability See What Others Are Saying!
  • Question
  • A speaks truth in 60% of the cases and B in 80% of the cases. In what percentage of cases are they likely to contradict each other, narrating the same incident?


  • Options
  • A. 70%
  • B. 36%
  • C. 22%
  • D. 44%

  • Correct Answer
  • 44% 

    Explanation

    Let A = Event that A speaks the truth
    and B = Event that B speaks the truth
    Then, P(A) = 60/100 = 3/5 and P(A) = 80/100 = 4/5
    ? P(A) = (1 - 3/5) = 2/5 and
    P(B) = (1 - 4/5) = 1/5

    P(A and B contradict each other)
    = P [(A speaks the truth and B tells a lie) or (A tells a lie and B speak the truth)]
    =P[(A and B) or (A and B)]
    =P(A and B) + P (A and B)
    = P(A) x P(B) + P(A) x P(B)
    = (3/5 x 1/5) + ( 2/5 x 4/5)
    = (3/25 + 8/25 ) = 11/25
    = (11/25 x 100)% = 44%


  • More questions

    • 1. Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:

    • Options
    • A. 2 : 3
    • B. 4 : 3
    • C. 6 : 7
    • D. 9 : 16
    • Discuss
    • 2. A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?

    • Options
    • A. 40 sec
    • B. 42 sec
    • C. 45 sec
    • D. 48 sec
    • Discuss
    • 3. A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is:

    • Options
    • A. 45 m
    • B. 50 m
    • C. 54 m
    • D. 72 m
    • Discuss
    • 4. If the number 91876 * 2 is completely divisible by 8, then the smallest whole number in place of * will be:

    • Options
    • A. 1
    • B. 2
    • C. 3
    • D. 4
    • E. None of these
    • Discuss
    • 5. A boy multiplied 987 by a certain number and obtained 559981 as his answer. If in the answer both 9 are wrong and the other digits are correct, then the correct answer would be:

    • Options
    • A. 553681
    • B. 555181
    • C. 555681
    • D. 556581
    • Discuss
    • 6. The least number which should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3 is:

    • Options
    • A. 3
    • B. 13
    • C. 23
    • D. 33
    • Discuss
    • 7. (17)3.5 x (17)? = 178

    • Options
    • A. 2.29
    • B. 2.75
    • C. 4.25
    • D. 4.5
    • Discuss
    • 8. 
      The number of odd days in a leap year is?

    • Options
    • A. 1
    • B. 2
    • C. 3
    • D. 4
    • Discuss
    • 9. 
      16, 4, 2, 1.5, 1.75, 1.875

    • Options
    • A. 1.875
    • B. 1.75
    • C. 1.5
    • D. 2
    • Discuss
    • 10. 
      In a circus there was a leopard and a tiger walking in the two different rings of same radii. There I observed that when leopard moved 3 steps, tiger moved 5 steps in the same time,but the distance traversed by leopard in 5 step is equal to the distance traversed by tiger in 4 steps. what is the number of rounds that a leopard made when tiger completed 100 rounds?

    • Options
    • A. 120
    • B. 48
    • C. 75
    • D. none of these
    • Discuss


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