Question 8165 – GATE 2015 [Set-1]

75% of students have a chance of passing atleast one subject
= 1 – (1 – m) (1 – p) (1 – c) = 0.75 —-(i)

50% of students have a chance pass in atleast two
(1 – m)pc + (1 – p)mc + (1 – c) mp + mpc = 0.5 —-(ii)
40% of students have a chance of passing exactly two
(1 – m)pc + (1 – p)mc + (1 – c)mp = 0.4 —-(iii)
From equation (ii) and (iii) we can get
mpc = 0.1
⇒ m*p*c = 1/10
Statement (III) is correct.
→ Simplify eq (i), we get
⇒ p+c+m – (mp+mc+pc) + mpc = 0.75
⇒ p+c+m – (mp+mc+pc) = 0.65 —-(iv)
→ Simplify equation (iii), we get
⇒ pc + mc + mp – 3mpc = 0.4 <br pc="" +="" mc="" mp="0.7" —-(v)=""
From (iv) and (v)
p + c + m – 0.7 = 0.65
⇒ p + c + m = 1.35 = 27/20
Statement (I) is correct.