The probabilities that a student passes in Mathematics,Physics and Chemistry are m, p and 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 a 40% chance of passing in exactly two. Which of the following relations are true?

Options

A. `p+m+c=(19)/(20)`
B. `p+m+c=(27)/(20)`
C. `pmc=(1)/(10)`
D. `pmc=(1)/(4)`

Answer

A, B, C, D

Explanation

We have,
`P(AB cup C)=(3)/(4)`
i.e., `P(A)+P(B)+P(C )-P(A cap B)-P(B cap C)-P(A cap C)+P(A cup B cup C)=(3)/(4)`
`P(A cap B)+P(B cap C)+P(A cap C)-2P(A cap B cap C)=(1)/(2)`
and,
`P(A cap B)+P(B cap C)+P(A cap C)-3P(A cap B cap C)=(2)/(5)`
From (ii) and (iii), we get
`P(A cap B cap C)=(1)/(2)-(2)/(5)=(1)/(10)`
`implies P(A)P(B)P(C )=(1)/(10) implies " pmc " =(1)/(10)`
From (i), (ii) and (iii), we have
`P(A)+P(B)+P(C )-((1)/(2)+(2)/(10))+(1)/(10)=(3)/(4) implies p+m+c=(27)/(20)`