Question

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 atleast one, a 50% chance of passing in atleast two, and a 40% chance of passing in exactly two. Which of the following relation is true?

• A. p + m + c = $\frac { 19 } { 20 }$
• B. p + m + c = $\frac { 27 } { 20 }$
• C. p m c = $\frac { 1 } { 5 }$
• D. p m c = $\frac { 1 } { 4 }$

Answer 1

Answer: (B)

p + m + c = $\frac { 27 } { 20 }$

Answer 2

We have,

P (A Č B Č C) = $\frac { 3 } { 4 }$

i.e., P (1) + P (2) + P (3) = P (A Ē B) – P (B Ē C) –

P (A Ē C) + P (A Ē B Ē C) = $\frac { 3 } { 4 }$… (1)

P (A Ē B) + P (B Ē C) + P (A Ē C)

– 2 P (A Ē B Ē C) = $\frac { 1 } { 2 }$ … (2)

and P (A Ē B) + P (B Ē C) + P (A Ē C)

– 3 P (A Ē B Ē C) = $\frac { 2 } { 5 }$ … (3)

From (2) and (3), we get P (A Ē B Ē C) = $\frac { 1 } { 2 }$ – $\frac { 2 } { 5 }$ = $\frac { 1 } { 10 }$

… (4)

Ž P (1) P (2) P (3) = $\frac { 1 } { 10 }$ Ž p m c = $\frac { 1 } { 10 }$ .

From (1), (2) and (3), we have

P (1) + P (2) + P (3) – $\left( \frac { 1 } { 2 } + \frac { 2 } { 10 } \right)$ + $\frac { 3 } { 4 }$

Ž p + m + c = $\frac { 27 } { 20 }$ .

Hence (2) is correct answer