The probabilities that a student passes in mathematics, physics and chemistry are m, p and c respectively of these subjects the students 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. Which of the following
relations are true?

Question

Infinity Learn · Accepted Answer

We have P(A∪B∪C)=34 I.e, P(A)+P(B)+P(C)−P(A∩B)−P(B∩C)−P(C∩A)+P(A∩B∩C)⟶(i)P(A∩B)+P(B∩C)+P(A∩C) −2P(A∩B∩C)=12⟶( ii )And P(A∩B)+P(B∩C)+P(A∩C)−3P(A∩B∩C)=25⟶( iii )From eq’s (ii) and (iii) we getP(A∩B∩C)=12−25=110⟶(iv)P(A)P(B)P(C)=110PMC=110From eq’s (i) ,(ii) and (iii) we haveP(A)+P(B)+P(C)−12+210+110=34P+m+c=2720

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