MATH SOLVE

2 months ago

Q:
# 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).

Accepted Solution

A:

Answer:Yes, because the P(A) · P(B) = P(A and B) ⇒ last answerStep-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)