Question

In an examination, 70% students passed in physics, 80% students passed in chemistry, 75% students passed in mathematics and 85% students passed in biology, and x% students failed in all for the four subjects. what is the minimum value of x?

Answer 1

P(failing in Physics) = 30% = $\frac{30}{100}$ = 0.3

P(failing in Chemistry) = 20% = $\frac{20}{100}$ = 0.2

P(failing in Maths) = 25% = $\frac{25}{100}$ = 0.25

P(failing in Biology) = 15% = $\frac{15}{100}$ = 0.15

Now, since x% students failed in all for the four subjects. We have to find the  minimum value of x.

P(failing in all 4 subjects) = $0.3 \times 0.2 \times 0.25 \times 0.15$

= 0.00225

Percent of students failing in all 4 subjects = 0.00225 x 100%

= 0.225%

So, the minimum value of x is 0.225%.