MATH SOLVE

3 months ago

Q:
# PLEASE HELP!!Let Events A and B be described as follows:P(A) = doing yard workP(B) = it rainingThe probability that it will rain this weekend is 68% The probability of doing yard work this weekend and it raining is 15%. If the probability of doing yard work is 53%, are doing yard work and it raining independent?A. Yes, because P(A | B) = 0.22 and the P(A) = 0.53are not equal.B. No, because P(A| B) = 0.28 and the P(B) = 0.68 are not equal.C. Yes, because because P(A| B) = 0.28 and the P(B) = 0.68 are not equal.D. No, because P(A | B) = 0.22 and the P(A) = 0.53are not equal.

Accepted Solution

A:

Answer:D. No, because [tex]P(A|B)=0.22[/tex] and the [tex]P(A) = 0.53[/tex] are not equal.Step-by-step explanation:Given:Probability of doing yard work is, [tex]P(A)=53\%=0.53[/tex]Probability of raining, [tex]P(B)=68\%=0.68[/tex]Probability of doing yard work and it raining is, [tex]P(A\cap B)=15\%=0.15[/tex]Now, two events A and B are independent if,[tex]P(A|B)=P(A);P(B|A)=P(B)[/tex]Conditional probability of event A given that B has occurred is given as:[tex]P(A|B)=\frac{P(A\cap B}{P(B)}\\P(A|B)=\frac{0.15}{0.68}=0.22[/tex]So, [tex]P(A|B)=0.22\ and\ P(A)=0.53[/tex]Since, [tex]P(A|B)\ne P(A)[/tex], A and B are not independent events.