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Question

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

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Solution

The correct options are

**B** p+m+c=2720

**C** pmc=110

Referring to the illustration:

Let s, t, u, v, w, x, y and z are the probabilities of the respective regions.

Thus, we have:

s+t+u+v+w+x+y=0.75 ...(i)

v+w+x+y=0.5 ...(ii)

v+w+x=0.4 ...(iii)

Thus, subtracting (ii) and (iii): y=pmc=0.1=110

Here, y refers to the intersection of all the three and hence equals p∗c∗m since they are independent events.

Again, subtracting (i) and (ii): s+t+u=0.25

We need to find m+c+p:

m+c+p=s+t+u+2(v+w+x)+3y=0.25+2∗0.4+3×0.1=1.35=2720

Hence, (b), (c) are correct.

Referring to the illustration:

Let s, t, u, v, w, x, y and z are the probabilities of the respective regions.

Thus, we have:

s+t+u+v+w+x+y=0.75 ...(i)

v+w+x+y=0.5 ...(ii)

v+w+x=0.4 ...(iii)

Thus, subtracting (ii) and (iii): y=pmc=0.1=110

Here, y refers to the intersection of all the three and hence equals p∗c∗m since they are independent events.

Again, subtracting (i) and (ii): s+t+u=0.25

We need to find m+c+p:

m+c+p=s+t+u+2(v+w+x)+3y=0.25+2∗0.4+3×0.1=1.35=2720

Hence, (b), (c) are correct.

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