Question

Determine if the events A and B are independent. Show all steps.

P(A) =2/5
P(B) =1/5
P(A and B) = 2/5​

Answer 1

Answer:

`P(A U B ) = (13)/(25)`

Explanation:

STEP:-1

Given that events A and B are independent then

P(A ∩B ) = P(A) P(B)

Given that P(A) = 2/5 and P(B) = 1/5

STEP:- 2

P(A ∩B ) = P(A) P(B)

`P(A U B) = P(A) +P(B) - P(A n B )`

`P(A U B ) = P(A) +P(B) - P(A) P(B)`

Step(iii):-

`P(A U B ) = (2)/(5) +(1)/(5) - (2)/(5) X (1)/(5)`

`P(A U B ) = (3)/(5) - (2)/(5) X (1)/(5)`

`P(A U B ) = (3)/(5) - (2)/(25)`

`P(A U B ) = (15-2)/(25) = (13)/(25)`