Question

For a group of students, 30% ,40% and 50% failed in physics, chemistry and at least one of the two subjects respectively .If an examinee is selected at random, what is the probability that he passed in physics if it is known that he failed in chemistry

Answer 1

$Answer:P(\text{ he passed in physics given that he failed in chemistry})=\frac{1}{2}$

Explanation:

Let the total number of students = 100

Number of students failed in physics = 30% of 100 =30

Number of students failed in chemistry = 40% of 100 =40

Number of students failed at least one of the two subjects = 50% of 100 =50

We need to calculate

$P(\text{ he passed in physics given that he failed in chemistry})\\\\=\frac{P(\text{passed in physics but failed in chemistry)}}{P(\text{  failed in chemistry})}$

First we calculate ,

$n(P\cup C)=n(P)+n(C)-n(P\cap C)\\\\50=30+40-n(P\cap C)$

$50-70=-n(P\cap C)\\20=n(P\cap C)$

now,

$n(\text{ passed in physics but failed in chemistry})=n(C-P)\\\\=n(C)-n(P\cap C)\\\\=40-20\\\\=20$

So,

$P(\text{ he passed in physics given that he failed in chemistry})\\\\\\=\frac{P(C-P)}{P(C)}\\=\frac{\frac{20}{100}}{\frac{40}{100}}\\\\=\frac{1}{2}$

Answer 2

Answer:

1/2

Step-by-step explanation:

click on above photo