Question

The odds in favour of one student passing a test are 3:7 .The odds against another student passing it are 3:5 . What is the probability that both pass the test

Answer 1

Answer:

Probability = $\frac{6}{35}$

Step-by-step explanation:

In the question,

Probability of passing a test by one student = $\frac{3}{7}$

Probability of failing a test by another student = $\frac{3}{5}$

So,

The probability of this student to pass the test = $1-\frac{3}{5}=\frac{2}{5}$

So,

The probability to pass the test by both the students is given by,

= $\frac{3}{7}\times \frac{2}{5}=\frac{6}{35}$

So,

Probability = $\frac{6}{35}$

Therefore, the probability of both the students to pass the test is $\frac{6}{35}$.

Answer 2

Answer:

{odds in favour of A}=p(A)/p(A`)

=3/7

p(A) +p(A`)=1

p(A) =p(A`)-1

therefore:p(A) /1-p(A)

=3/7

7 p(A) = 3 (1- p(A))

7p(A) = 3 - 3p(A)

10 p(A) =3= p(A)

p(A) = 3/10

{odds in favour of B}=3/5

p(B) /p(B`) =3/5

1- p(B) /p(B`) = 3/5

5 -5 p(B) = 3 p(B)

5= 8p(B)

p(B) = 5/8

therefore p(AnB) =p(A). p(B)

=[3/10].[5/8] =3/16

Answer= 3/16