Q1 / 108 · NTA Abhyas (JEE Main) 2020 · Mathematics · Probability

Probability that A will pass the exam is 14, B will pass the exam is 25 and  C will pass the exam is 23. The probability that exactly one of them will pass the exam is

  • A
    25
  • B
    320
  • Correct answer
    C
    920
  • D
    45

Solution

PA=14,PB=25,PC=23
∵A,B,C are independent events, then
the probability that exactly one of them passes
=PA∩BC∩CC+PAC∩B∩CC+PAC∩BC∩C
=PA⋅PBC⋅PCC+PAC⋅PB⋅PCC+PACPBC⋅PC
=14×35×13+34×25×13+34×35×23=920

Hence, the correct answer is option: 'C'.

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