Question

Consider two events such that P(A) = equals 3/5 , P(B) = 2/3 , and P(A ∩ B) = 1/5 . Are events A and B independent events?

Yes, they are independent because P(A) ⋅ P(B) = P(A ∩ B)
No, they are dependent because P(A) ⋅ P(B) ≠ P(A ∩ B)
Yes, they are independent because P(A) ⋅ P(B) ≠ P(A ∩ B)
No, they are dependent because P(A) ⋅ P(B) = P(A ∩ B)

Answer 1

Option B

Explanation:

Option A should be true if they are independent

• P(A)P(B)
• 3/5×2/3
• 2/5≠1/5

So

They are dependant

Answer 2

Option 2

Explanation:

Checking whether P(A) × P(B) = P(A∩B) :

• 3/5 x 2/3 = 1/5
• 2/5 ≠ 1/5

Since this does not obey the Multiplication rule of probability, these events are not independent.

So, the answer is :

No, they are dependent because P(A) ⋅ P(B) ≠ P(A ∩ B)