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. $p+m+c=\frac{19}{20}$
• B. $p+m+c=\frac{27}{20}$
• C. $pmc=\frac{3}{10}$
• D. $pmc=\frac{1}{4}$

Answer 1

Answer: (B)

$p+m+c=\frac{27}{20}$

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 $=a+b+c+d=0.5$
$\therefore d=0.1$
Chance of passing in at-least one subject $=x+y+z+a+b+c+d=0.75$
$\therefore x+y+z=0.25$
Now, $p+m+c=(x+y+z)+2(a+b+c)+0.3=1.35=\frac{27}{20}$
$pmc=(x+a+b+d)(y+b+c+d)(z+a+c+d)$
We do not have enough data, so can't proceed further.