Question:
✍ None You can view the question in original Chegg URL page.
Expert answer: 0 0
✍ None
Step: 1
Given:
A Venn diagram displays the probabilities of events A, B, and C.
Explanation
Conditional probability represents the likelihood of an event when another event has occurred.
Step: 2
a. The Probability P(A|B) is calculated as,
P(A|B) = (P(B|A) ∗ P(A))/(P(B))
= (0.9 ∗ 0.1)/(0.2)
Explanation
Bayes' theorem is a fundamental principle in probability theory that describes how probabilities are updated or revised based on new evidence or information.
Step: 3
b. The Probability P(C|B) is calculated as,
c. The probability P(B|A U C) is calculated as,
= 0.09/0.2
= 0.45
P(C|B) = (P(B|C) ∗ P(C))/(P(B))
= (0.8 ∗ 0.2)/0.2
= 0.16/0.2
= 0.8
P(B|AUC) = (P(B|A). P(A) + P(B|C). P(C))/(P(AUC
= (0.9 ∗ 0.1 + 0.8 ∗ 0.2)/(0.1 + 0.2 − 0.2)
= (0.09 ∗ 0.16)/(0.1)
= 0.144
Step: 4
d. The Probability P(B|A,C) is calculated as,
Explanation
The probability of event B happening given that both event A and C.
Final Answer
a. P(A|B)=0.45 b.P(C|B)=0.8
c.P(B|A U C)=0.144 d. P(B|A,C)=P(B|A∩ C)
None
