The probabilities that a student pass in Mathematics, Physics and Chemistry are $m$, $p$, $c$ respectively. Of these subjects the student has a 75 % chance of passing in at least one, a 50% chance of passing in at least two and 40 % chance of passing in exactly two.

Which of the following relations are true

• 1 - (1 - m) (1 - p) (1 - c) = 0.75 -------(1)
  (1 - m)pc + (1 - p)mc + (1 - c)mp + mpc = 0.5 -------(2)
  (1 - m)pc + (1 - p)mc + (1 - c)mp = 0.4 -------(3)
  
  From last 2 equations, we can derive mpc = 0.1
  
  After simplifying equation 1, we get.
  p + c + m - (mp + mc + pc) + mpc = 0.75
  p + c + m - (mp + mc + pc) = 0.65 -------(4)
  
  After simplifying equation 3, we get
  pc + mc + mp - 3mpc = 0.4
  
  Putting value of mpc, we get
  pc + mc + mp = 0.7
  
  After putting above value in equation 4, we get
  p + c + m - 0.7 = 0.65
  p + c + m = 1.35 = 27/20
  
• 8 years agoHelpfull: Yes(0) No(0)