Engineering probability question

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SUMMARY

The discussion focuses on a complex probability problem involving events A1, A2, and A3 with specific probabilities provided. Key calculations include determining the probabilities of eight events B1, B2, and B3, calculating P[A3], and finding the probabilities of exactly one and two or more events occurring. Additionally, the conditional probability of all events occurring given that two or more have occurred is also addressed. The discussion emphasizes the importance of showing work and relevant equations for effective assistance.

PREREQUISITES
  • Understanding of basic probability concepts, including conditional probability.
  • Familiarity with Venn diagrams for visualizing events and their intersections.
  • Knowledge of probability notation, including complements (A*) and intersections (A n B).
  • Ability to apply the law of total probability in complex scenarios.
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  • Study the law of total probability to understand how to calculate overall probabilities from conditional probabilities.
  • Learn how to construct and analyze Venn diagrams for multiple events.
  • Explore conditional probability calculations, particularly in scenarios with multiple events.
  • Review examples of solving complex probability problems to enhance problem-solving skills.
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Students and professionals in mathematics, statistics, or data science who are looking to deepen their understanding of probability theory and its applications in real-world scenarios.

skhanal1
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hello everyone, I had a multiple part question to a probability problem

Events A1, A2 and A3 are such that:
P[A1] = 3/10
P[A2|A1] = 6/10
P[A2|A1*]= 8/10
P[A3|A1 n A2] = 5/10
P[A3|A1* n A2] = 2/10
P[A3|A1 n A2*] = 7/10
P[A3|A1* n A2*] = 1/10

(i) Determine the probabilities of the eight events B1 n B2 n B3, where Bi = Ai or
Bi = Ai*, and mark them on the appropriate Venn diagram.
(ii) Determine P[A3].
(iii) What is the probability that exactly one of the events A1, A2 and A3 occurs?
(iv) What is the probability that two or more of the events A1, A2 and A3 occur?
(v) What is the conditional probability that all of the events A1, A2 and A3 occur, given
that two or more of them have occurred?

The '*' means complement and 'n' means intersection.

Appreciate any help.
 
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Hi, skhanal1. You have not posted your attempt at a solution yet. The PF rules state, you must list relevant equations yourself, and show your work; and then someone might check your math.
 

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