let a and b be two events with the following probabilities.\n- the probability that a occurs is 0.6.\n- the…

let a and b be two events with the following probabilities.\n- the probability that a occurs is 0.6.\n- the probability that b occurs is 0.9.\n- the probability that b occurs given that a occurs is 0.3.\nwhat is the conditional probability that a occurs given that b occurs?\nwrite your answer as a decimal. do not round.

let a and b be two events with the following probabilities.\n- the probability that a occurs is 0.6.\n- the probability that b occurs is 0.9.\n- the probability that b occurs given that a occurs is 0.3.\nwhat is the conditional probability that a occurs given that b occurs?\nwrite your answer as a decimal. do not round.

Answer

Answer:

0.2

Explanation:

Step1: Recall the formula for conditional probability

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

Step2: Find $P(A\cap B)$

Given $P(A) = 0.6$ and $P(B|A)=0.3$. So $P(A\cap B)=P(B|A)\times P(A)=0.3\times0.6 = 0.18$.

Step3: Recall the formula for the other - way conditional probability

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

Step4: Calculate $P(A|B)$

Given $P(B) = 0.9$ and $P(A\cap B)=0.18$. Then $P(A|B)=\frac{0.18}{0.9}=0.2$.