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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 ?

A
p+m+c=1920
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B
p+m+c=2720
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C
pmc=310
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D
pmc=14
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Solution

## The correct option is A p+m+c=2720As it can be seen from Venn diagram, that x+a+b+d=py+b+c+d=mz+a+c+d=cBut, chance of passing in exactly two subjects =a+b+c=0.4Chance of passing in at-least two subjects =a+b+c+d=0.5∴d=0.1Chance of passing in at-least one subject =x+y+z+a+b+c+d=0.75∴x+y+z=0.25Now, p+m+c=(x+y+z)+2(a+b+c)+0.3=1.35=2720pmc=(x+a+b+d)(y+b+c+d)(z+a+c+d)We do not have enough data, so can't proceed further.

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