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

Answered: Image /qna-images/answer/02a4359e-9a63-499e-ae65-33e2ce0f4196.jpg

Answered: (e) Consider a sequence of events A,,…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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According to Bayes' Theorem, the probability of event A, given that event B has occurred, is as follows. P(A) P(BA) P(A|B)= P(A) P(BA)+P(A').P(B| A') Use Bayes' Theorem to find P(A|B) using the probabilities shown below. 1 P(A) = P(A) = P(B| A)= ½, and P (B| A') = 2 The probability of event A, given that event B has occurred, is P(A| B) = ☐. (Round to the nearest thousandth as needed.)
8 Which statement below is not a basic probability rule for events A and B? A) P(entire sample space) = 1 B) For any event A: 0 s P(A) s1 C) Events A and B are mutually exclusive if P(A n B) = .1 D) Complement of A: P(not A) = 1- P(A) E) Events A and B are dependent events if P(B) is affected by event A
Let A denote the event of placing a $1 straight bet on a certain lottery and winning. Suppose that, for this particular lottery, there are 4,320 different ways that you can select the four digits (with repetition allowed) in this lottery, and only one of those four-digit numbers will be the winner. What is the value of P(A)? What is the value of P(A)? What is the value of P(A)? P(A)=(Round to five decimal places as needed.) n 777 I' ….…. ✓ Ş H 8 More X
A certain university has 16 vehicles available for use by faculty and staff. Four of these are vans and 12 are cars. On a particular day, only two requests for vehicles have been made. Suppose that the two vehicles to be assigned are chosen at random from the 16 vehicles available. (Enter your answers as fractions.) (a) Let E denote the event that the first vehicle assigned is a van. What is P(E)? (b) Let F denote the probability that the second vehicle assigned is a van. What is P(F | E)? (c) Use the results of parts (a) and (b) to calculate P(E n F).
A car is parked among N cars in a raw, not at either end. On his return the owner finds that exactly r of the N places are still occupied. What is the probability that both neighbouring places are empty?
A flush in the card game of poker occurs if a player gets five cards that are all the same suit (clubs, diamonds, hearts, or spades). Complete parts (a) and (b) to obtain the probability of being dealt a flush in five cards. (a) Initially concentrate on one suit, say clubs. There are 13 clubs in a deck. Compute P(five clubs) = P(first card is clubs and second card is clubs and third card is clubs and fourth card is clubs and fifth card is clubs). P(five clubs) = (Round to six decimal places as needed.)
In an experiment where 2 balls are drawn successively at random without replacement from a box containing 2 Red, 3 Green and 2 Blue Balls. Let R be the event that a ball drawn is red, B for blue and G for green. Which of the following represents the probability that the first is a red or a blue, followed by a green? P(R U B) x P(G) P(R U B) x P[G | (R U B)] P(R U B) + P(G) P(R U B) x P[(R U B) | G]
an ice-cream stall m + n (n ≤ m) people are in a queue to buy one |50 ice-cream each. The stall-keeper has no change. Precisely m of the people have just a |50 note and the remaining n people have just a |100 note. Find the probability that the stall-keeper always has enough change to serve the customers in turn.
1 Let A and B be events with P(A) = P(B) = " and P(AB) =. What is P[(ANB)U(BnA)]? None of these O 9/10 4/5 O 19/30
At a popular holiday destination, of the people are tourists. You randomly select two people from the population What is the probability that at least one of the two people is a tourist? Hint: P (TN or NT or TT) or 1- P(NN) O 7/16 O 9/16 O 8/16 O 10/16
Let A denote the event of placing a $1 straight bet on a certain lottery and winning. Suppose that, for this particular lottery, there are 4,320 different ways that you can select the four digits (with repetition allowed) in this lottery, and only one of those four-digit numbers will be the winner. What is the value of P(A)? What is the value of P(A)?
Prove the property

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