89.8k views
1 vote
Given P(A) = 0.3, P(B) = 0.6, and P(A|B) = 0.1, determine the following probabilities.

(a). P(A and B) =

(b) P(A or B) =

User Ccjmne
by
7.3k points

1 Answer

7 votes

Final answer:

To find P(A and B), we multiply P(A|B) by P(B), resulting in 0.06. P(A or B) is computed using the formula for the union of two events, resulting in 0.84.

Step-by-step explanation:

The student asked to determine the probabilities of P(A and B) and P(A or B), given that P(A) = 0.3, P(B) = 0.6, and P(A|B) = 0.1.

To find P(A and B), we use the definition of conditional probability: P(A|B) = P(A and B) / P(B). This yields P(A and B) = P(A|B) * P(B) = 0.1 * 0.6 = 0.06. For P(A or B), we use the formula for the probability of the union of two events: P(A or B) = P(A) + P(B) - P(A and B), giving us P(A or B) = 0.3 + 0.6 - 0.06 = 0.84.

User BobFlemming
by
8.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories