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

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

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)=(P(A\cap B)/(P(B))\\P(A|B)=(0.15)/(0.68)=0.22`

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

Since,
`P(A|B)\\e P(A)`, A and B are not independent events.