Mathematics: 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

let events a and b be described as follows: p(a)

hi105

10.01.2022

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.

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DEVlN6070

15.04.2023

Table C

Step-by-step explanation:

When graphed, it passes vertical line test.

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