Question

Let E and F be two independent events . the probability that both E and F happen is 1/12 and the probability that neither E nor F happens is 1/2 then a value of p(E)/ p( F) is

Answer 1

Answer:

4/3

Step-by-step explanation:

Let :

P(E) = x

P(F) = y

P(E and F) = xy = 1/12.................i)

P(E not happening) = 1 - x

P(F not happening) = 1 - y

P(E and F not happening) = (1 - x) (1 - y) = 1/2........ii)

From i:

x = 1/12y

Replace this value in ii)

(1 - 1/12y)(1 - y) = 1/2

Open the brackets:

1 - 1/12y - y + 1/12 = 1/2

Solving by collecting the like terms together we get:

-1/12y - y = - 7/12

Multiply through by 12 y we have :

-1 - 12y^2 = - 7y

We form a quadratic equation :

12y^2 - 7y + 1 = 0

Solve for y by getting the roots :

12y^2 - 3y - 4y + 1 = 0

3y(4y - 1) - 1(4y - 1) = 0

(3y - 1)(4y - 1) = 0

3y = 1 or 4y = 1

y = 1/3 or 1/4

If we take 1/4 then x will be :

1/4x = 1/12

x = 1/3

P(E)/ P(F) = 1/3 ÷ 1/4

= 1/3 × 4/1 = 4/3

Answer 2

Answer:

4/3

Step-by-step explanation:

Let :

P(E) = x

P(F) = y

P(E and F) = xy = 1/12.................i)

P(E not happening) = 1 - x

P(F not happening) = 1 - y

P(E and F not happening) = (1 - x) (1 - y) = 1/2........ii)

From i:

x = 1/12y

Replace this value in ii)

(1 - 1/12y)(1 - y) = 1/2

Open the brackets:

1 - 1/12y - y + 1/12 = 1/2

Solving by collecting the like terms together we get:

-1/12y - y = - 7/12

Multiply through by 12 y we have :

-1 - 12y^2 = - 7y

We form a quadratic equation :

12y^2 - 7y + 1 = 0

Solve for y by getting the roots :

12y^2 - 3y - 4y + 1 = 0

3y(4y - 1) - 1(4y - 1) = 0

(3y - 1)(4y - 1) = 0

3y = 1 or 4y = 1

y = 1/3 or 1/4

If we take 1/4 then x will be :

1/4x = 1/12

x = 1/3

P(E)/ P(F) = 1/3 ÷ 1/4

= 1/3 × 4/1 = 4/3