Question

Let Events A & B be described as follows: P(A) = watching a movie P(B) = going out to dinner The probability that a person will watch a movie is 62% and the probability of going out to dinner is 46%. The probability of watching a movie and going out to dinner is 28.52% Are watching a movie and going out to dinner independent events? No, because the P(A) + P(B) ≠ P(A and B). Yes, because the P(A) + P(B) is greater than 100%. No, because the P(A)P(B) ≠ P(A and B). Yes, because the P(A)P(B) = P(A and B).

Answer 1

Yes, because the P(A) · P(B) = P(A and B) ⇒ last answer

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)