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  • Question
  • 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

  • Correct Answer
  • pmc = 1/10 

    Explanation

    P(M) = m, P (p) = p, P(c) = c
    ? The probability of at least one success
    = P (M ? P ? C)
    = m + p + c -mp - mc - pc + mcp = 3/4 ...(1)

    The probability of at least two successes = mcp + mcp + mcp + mcp
    = mc(1 - p) + mp (1 - c ) + (1 - m )cp + mcp
    = mc + mp + cp - 2mcp = 1/2

    The probability of exactly two success
    = mcp + mcp + mcp
    = mc(1 - p) + mp (1 - c ) cp(1 - m )
    = mc + mp + cp - 3 mcp = 2/5

    (2) & (3) gives,

    ? mcp = 1/2 - 2/5 = 1/10
    ? mc + mp + cp = 2/10 + 1/2 = 1/5 + 1/2 = 7/10


    From (1),

    m + p + c - 7/10 + 1/10 = 3/4
    ? m + p + c = 3/4 + 7/10 - 1/10 = 27/20
    Thus, pmc = 1/10 is a true relation.


  • Probability problems


    Search Results


    • 1. 
      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
    • 2. 
      A fair coin is tossed 100 times . The probability of getting tails an odd number of times is?

    • Options
    • A. 1/2
    • B. 1/8
    • C. 3/8
    • D. None of these
    • Discuss
    • 3. 
      If the probability for A fail in an examination is 0.2 and that for B is 0.3, then the probability that either A or B fails is?

    • Options
    • A. 0.38
    • B. 0.44
    • C. 0.50
    • D. 0.94
    • Discuss
    • 4. 
      What is the probability that a leap year selected randomly will have 53 Mondays?

    • Options
    • A. 2/7
    • B. 5/7
    • C. 1/7
    • D. Data inadequate
    • Discuss
    • 5. 
      What is the probability that a leap year selected randomly will have 53 Mondays?

    • Options
    • A. 2/7
    • B. 5/7
    • C. 1/7
    • D. Data inadequate
    • Discuss
    • 6. 
      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
    • 7. 
      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
    • 8. 
      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
    • 9. 
      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%
    • Discuss
    • 10. 
      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


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