Answer:
Yes, because the P(A) · P(B) = P(A and B) ⇒ last answer
Step-by-step explanation:
* Lets study the meaning independent and dependent 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)
* Lets solve the question
∵ P(A) = watching a movie
∵ P(B) = going out to dinner
∵ The probability that a person will watch a movie is 62%
∴ P(A) = 62% = 62/100 = 0.62
∵ The probability of going out to dinner is 46%
∴ P(B) = 46% = 46/100 = 0.46
∵ The probability of watching a movie and going out to dinner
is 28.52%
∵ P(A and B) = 28.52% = 28.52/100 = 0.2852
- Lets find the product of P(A) and P(B)
∵ P(A) = 0.62
∵ P(B) = 0.46
∵ P(A and B) = 0.2852
∴ P(A) · P(B) = 0.62 × 0.46 = 0.2852
∴ P (A and B) = P(A) · P(B)
∴ Watching a movie and going out to dinner are independent events
because the P(A) · P(B) = P(A and B)
