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  • 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%


  • Probability problems


    Search Results


    • 1. 
      Two dice and two coins are tossed. The probability that both the coins show head and the sum of the numbers found on the two dice is a prime number is?

    • Options
    • A. 5/72
    • B. 1/12
    • C. 13/144
    • D. 5/48
    • Discuss
    • 2. 
      If n integer taken at random are multiplied together then the probability that the last digit of the product is 2, 4, 6, 8 is?

    • Options
    • A. 2n/5n
    • B. 4n - 2n / 5n
    • C. 4n/5n
    • D. 8n - 4n / 5n
    • Discuss
    • 3. 
      If the integer m and n are chosen at random between 1 and 100, then the probability that a number of the from 7 m + 7 n is divisible by 5 equals?

    • Options
    • A. 1/4
    • B. 1/7
    • C. 1/8
    • D. 1/49
    • Discuss
    • 4. 
      The probability that 9 students pass in Mathematics, Physics and Chemistry are m, p and c respectively, of these subject the students has a 75% chance of passing in at least one subject 50% chance of passing in at least two subject and 40% chance of passing in exactly two. Which of the following relation are true?

    • Options
    • A. p + m + c =19/20
    • B. p + m + c = 17/20
    • C. pmc = 1/10
    • D. pmc = 1/4
    • Discuss
    • 5. 
      A natural number is selected at random from the set x = { x : 1 ? x ? 100 }. The probability that the number satisfies the inequality x 2 - 13x ? 30 is?

    • Options
    • A. 5/9
    • B. 9/50
    • C. 3/20
    • D. 7/9
    • Discuss
    • 6. 
      The probability that a leap year selected at random contains 53 Sundays, is

    • Options
    • A. 7/366
    • B. 26/183
    • C. 1/7
    • D. 2/7
    • Discuss
    • 7. 
      From 4 children, 2 women and 4 men, 4 person are selected. The probability that there are exactly 2 children among the selected persons, is

    • Options
    • A. 11/21
    • B. 9/21
    • C. 10/21
    • D. 5/21
    • Discuss
    • 8. 
      The probability that a man can hit a target is 3/4. He tries 5 times. The probability that he will hit the target atleast three times, is

    • Options
    • A. 291/364
    • B. 371/464
    • C. 471/502
    • D. 459/512
    • Discuss
    • 9. 
      A dice is rolled three times and sum of three numbers appearing on the uppermost face is 15. The chance that the first roll was four is

    • Options
    • A. 2/5
    • B. 1/5
    • C. 1/6
    • D. None of these
    • Discuss
    • 10. 
      If a 4- digit number is formed at random using the digit 1, 3, 5, 7 and 9 without repetition, then the probability that it is divisible by 5, is

    • Options
    • A. 4/5
    • B. 3/5
    • C. 1/5
    • D. 2/3
    • Discuss


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