(e) Consider a sequence of events A,, A2, ... , A, and define B to be the intersection of the events A up to Ak, i.e. BR = A N A2 n N Ag. Prove, by mathematical induction, that the following conditional probability expression P(B,) = P (A,)× P(A2\B1) × P(A3 \B2) × …·× P(A,|Bn-1) is true for all positive integers n > 1.

Q: 22 customers are eating dinner at an Italian restaurant. Of the 22 customers, 18 order pizza, 10…

A: Thank you for posting the question. As your question has more than 3 parts, as per the policy, we…

Q: Let A be the event that your hole cards are AK, and let B be the event that your hole cards are both…

A: P(A) =P(event of holding ace and king) = 452×452=162704 P(B) = P(event of holding are red ) = 2352

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Q: (3) P(A| B) > 0, i.e., the conditional probability is always non-negative.

A:

Q: Theorem 3-13. Necessary and sufficient condition for independence of n events A1, A2, ..., An is…

A:

Q: conditions (N,F,P) if n ≥ 2. P (^A;) = P(A₁)P(A2|A₁)P(A3|4₁ | A₂2) ···P(An|A₁ Ñ…-··Ñ An−1), i=1 n-1…

A: The theorem you mentioned is known as the "Multiplicative Law of Probability" or the "Chain Rule" of…

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Q: a) A(n) 3 of (Diamond)s? b) A Heart or Diamond? c) A number smaller than 5 (counting the ace as a…

A: A classic deck of 52 cards were given.

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A: Given that,we have to find when the general multiplication rule as applied to events A and B.Options…

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A:

Q: Two cards are randomly chosen without replacement from a ordinary deck of 52 cards. Let B be the…

A: In the particular problem, out of 52 cards the randomly chosen cards are 2 where the event BB…

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A: The information provided in the question are as follows :-and

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A:

Q: Let A denote the event of placing a ​$1 straight bet on a certain lottery and winning. Suppose​…

A: Given that there are total 2940 ways to choose four digit number.  So n= 2940.  But the only one of…

Q: A recent census found that 51.9% of adults are​ female, 10.4% are​ divorced, and 5.9% are divorced…

A: Let F be the event that the person is femaleD be the event that the person is divorced.

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A: There are 6 even and 6 odd numbers are there.

Q: Let S be the event that a randomly selected college student has taken a statistics course, and let C…

A: Given:

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A: We have given that  Number of vans = 4 Total number of vehicles = 12

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Q: n servers are located in a computer cluster. After one year, each server independently is still…

A: we can solve this problem using the Binomial Distribution.Here's the breakdown:What we are looking…

Q: According to Bayes' Theorem, the probability of event A, given that event B has occurred, is as…

A: According to the provided information, The Bayes theorem is defined as:

Q: Let A denote the event of placing a $1 straight bet on a certain lottery and winning. Suppose that,…

A:

Q: Bayes' theorem for an 'AND’ combined event is: Pr( A 'AND' B) = Pr( A|B )*Pr( B ). When does this…

A: We have given the following statement about the  Bayes  theorem.

Q: 5. Let A and B be two events such that P(A) = 1/7, P(AUB) = 1/2, and P(AB) = 1/12. Determine P(B).…

A: ANS Given Let A and B be two events                P(A)=17 ,  P(A∪B) =12,     P(AB)=112 =P(A∩B)…

Q: Given  P(A) = 0.3, P(b) = 0.5 and P( A and B ) = 0.2.       Are the events A,B independent ?…

A: Thank you for posting the question. Since you have asked multiple question(Different questions), we…