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?

Explanation

The correct options are

B `p+m+c=frac{27}{20}`

C `_p m c=frac{1}{10}`

Let `M, P` and `C` be the events of passing in mathematics, physics and chemistry respectively.

`P(M cup P cup C)=frac{75}{100}=frac{3}{4}`

`P(M cap P)+P(P cap C)+P(M cap C)-2 P(M cap P cap C)=frac{50}{100}=frac{1}{2}`

`P(M cap P)+P(P cap C)+P(M cap C)-3 P(M cap P cap C)=frac{40}{100}=frac{2}{5}`

`therefore m(1-p)(1-c)+p(1-m)(1-c)+c(1-m)(1-p)+mp(1-c)+mc(1-p)+pc(1-m)+` `=frac{3}{4}`

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