The probabilities that a student passes in Mathematics, Physics and Chemistry are m, p and c respectively. Of these subjects, the student has 75% chance of passing in at least one, a 50% chance of passing in at least two and a 40% chance of passing in exactly two. Following relations are drawn in m, p and c:
1. p + m + c = 27/20 2. p + m + c = 13/20 3. (p) × (m) × (c) = 1/10
(A) Only relation 1 is true
(B) Only relation 2 is true
(C) Relations 2 and 3 are true
(D) Relations 1 and 3 are true
Answer: (D)
Explanation:
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