IIILet C₁. C₂...., C₁events form a partition of the sample space1+Let A,B be events such that P(B nC)>0 Vi= 1, 2,... show thatnP(AB)=P(ABC, P (CB)i=1(Hint: start by applying the total probability theorem to the event An B)

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Answered: Let C₁, C₂, C events form a partition…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

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A probability experiment is conducted in which the sample space of the experiment is s= 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15, Let event A(2,3,4,5) and event B(12,13,14 Assume that each outcome is equally likely. List the outcomes in A and B. Are A and B mutually exclusive?
3. A random variable X has the following probability distribution: 2 3 2k 3k 2K² Find (1) k, (ii) P(X 5), and (iv) P(0 ≤x≤ 5) PIA 7 4k² 307
Is it possible to show the probability of (A), (B), and (A and B) as well please!
Have you ever re-gifted? According to Webster's dictionary 're-gift is to give a gift you received to someone else. Suppose you take a random sample of 1000 adults and get the following results: Yes - Regifted No - Regifted Total 400 Female Male Total 160 240 400 240 360 600 600 1000 Which of the following statements is true? Select one: O The events Regift and Female are dependent because P(Regift) = P(Regift|Female). O The events Regift and Female are independent because P(Regift) = P(Regift|Female). %3! O The events Regift and Female are dependent because P(Regift) + P(Regift Female). O The events Regift and Female are independent because P(Regift) + P(Regift|Female).
of events A and B is given below. A A' Total B 50 25 75 B' 36 18 54 Total 86 43 129 Using the table above, answer the questions below A) What is P(A'|B)? B) What is P(B|A)? C) What is P(AUB)? D) Are the events A and B independent? Enter yes or no.
10. Let A and B be two independent events for which the probability of P(A) = 0.25 and P(B) = 0.6, find а. Р(A]B) )\ b. P(B|A) с. Р(АNB) P(AUB) d.
Look at the 4 probability rules beow , an provide a REAL LIFE example for each. Also, with a Real LIfe EXAMPLE, explain how Disjoint events CAN be dependent. Rule 1. The probability P(A) of any event A satisfies 0 ≤ P(A) ≤ 1. Rule 2. If S is the sample space in a probability model, then P(S) = 1. Rule 3. Two events A and B are disjoint if they have no outcomes in common and so can never occur together. If A and B are disjoint, P(A or B) = P(A) + P(B) This is the addition rule for disjoint events. Rule 4. For any event A, P(A does not occur) = 1 − P(A)
3 a) The events A and B are such that P(A) =0.3, P(B'| A) =0.8 and P(B| A')=0.4. Find P(AOB) and P(AUB). Hence, state with reason whether A and B are independent events. b) A box contains 5 balls labelled 1, 2, 3, 4 and 5. A player draws a ball from the box randomly. If the number on the ball drawn is 2, 3 or 4, the players score is that number. If the number on the ball is 1 or 5, the player can draw a second ball without replacing the first ball, and his score is the sum of the numbers on the two balls. The events A and B are defined as follows A: The score of a player is 4, 5, 6 or 7. B: A player draws two balls from the box. Find P(A), P(B), P(ANB) and P(AUB).
Prove the property
A car dealer is trying to sell five used cars. She attempts to sell a car to each customer that walks in. Suppose that only 7% of all the potential customers are willing and able to purchase a car, and assume that each customer acts independently of one another. Let X denote the number of customers that walk in before all five cars are sold. What is the distribution of X? What is the probability that the last car is sold to the 100th customer?

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Let C₁, C₂, C events form a partition of the sample space Let A,B be events such that P(B nC)>0 Vi=1, 2, n show that P(A/B)=P(AB n C)P (C,B) inl (Hint: start by applying the total probability theorem to the event AnB)