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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=2720
As it can be seen from Venn diagram, that
x+a+b+d=p
y+b+c+d=m
z+a+c+d=c
But, chance of passing in exactly two subjects =a+b+c=0.4
Chance of passing in at-least two subjects =a+b+c+d=0.5
d=0.1
Chance of passing in at-least one subject =x+y+z+a+b+c+d=0.75
x+y+z=0.25
Now, p+m+c=(x+y+z)+2(a+b+c)+0.3=1.35=2720
pmc=(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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