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 ?

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 ?

  1. A

    p+m+c=1920

  2. B

    p+m+c=2720

  3. C

    pmc=110

  4. D

    pmc=14

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    Solution:

    P(mpc)=75100m+p+cmp+mpc=34(1)
    p(passing at least 2 subjects)
    =mp2mpc=50100=12(2)
    p(passing exactly 2 subjects)
    =mp3mpc=40100=25(3)
    (2) and (3) gives mpc=1225=110
    From (2)mp=12+2mpc=12+15=710
    Fromm=34+mpmpc
    =34+710110=15+14220=2720
     

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