Question

PLEASE HELP!!
Let Events A and B be described as follows:


P(A) = doing yard work
P(B) = it raining


The 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.

Answer 1

Answer:

D. No, because $P(A|B)=0.22$ and the $P(A) = 0.53$ are not equal.

Step-by-step explanation:

Given:

Probability of doing yard work is, $P(A)=53\%=0.53$

Probability of raining, $P(B)=68\%=0.68$

Probability of doing yard work and it raining is, $P(A\cap B)=15\%=0.15$

Now, two events A and B are independent if,

$P(A|B)=P(A);P(B|A)=P(B)$

Conditional probability of event A given that B has occurred is given as:

$P(A|B)=\frac{P(A\cap B}{P(B)}\\P(A|B)=\frac{0.15}{0.68}=0.22$

So, $P(A|B)=0.22\ and\ P(A)=0.53$

Since, $P(A|B)\ne P(A)$, A and B are not independent events.