Question

for events A and B, P(A)= 3/14 and P(B)= 1/5. Also, P(A and B)= 3/65. Are A and B independent events?

Answer 1

No, A and B are not independent events

Step-by-step explanation:

Let us study the meaning independent probability  

• Two events are independent if the result of the second event is not  affected by the result of the first event
• If A and B are independent events, the probability of both events  is the product of the probabilities of the both events  P (A and B) = P(A) · P(B)

∵ P(A) = $\frac{3}{14}$

∵ P(B) = $\frac{1}{5}$

∴ P(A) . P(B) = $\frac{3}{14}$ × $\frac{1}{5}$

∴ P(A) . P(B) = $\frac{3(1)}{14(5)}$

∴ P(A) . P(B) = $\frac{3}{70}$

∵ P(A and B) = $\frac{3}{65}$

∵ P(A) . P(B) = $\frac{3}{70}$

- The two answers are not equal

∴ P (A and B) ≠ P(A) · P(B)

- In independent events P (A and B) = P(A) · P(B)

∴ A and B are not independent events

No, A and B are not independent events

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