As a preliminary helper result, show by induction that for events E1, E2,...,EM, P(E, or E, or... or Em)s ¿ P(EM)

Q: given events Q and T, compute P (Q) if P(T and Q) =0.3 and P (T/Q) =0.6

A: provided that, P(T and Q) =0.3 and P (T/Q) =0.6 we use the formula, P (T/Q) = P( T and Q)/P(Q)

Q: Suppose that A and B are mutually exclusive events. a. Use the special addition rule to express P(A…

A: a. Events A and B are mutually exclusive. Special addition rule is used. Special Addition Rule If…

Q: Out of the 2000 students who attend a certain high school, 1400 students own cell phones, 1000 own a…

A: As per given by the question, there are 2000 student who attend a certain high school and out of…

Q: Prove that if P( A ) = 7/50 , P ( B ) = 1/4 and P(A U B) =3/10, then A and B are inclusive events

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Q: For any two events A and B and P(B) ÷ 1 and A N B = Ø, find weather the following statement is true…

A: If there are n mutually exclusive, exhaustive and equally likely outcomes of a random experiment and…

Q: Suppose that a finite class contains 50% freshmen, 20% sophomores, 10% juniors, and the rest…

A: Given: P (F) = 0.50 P (S) = 0.20 P (J) = 0.10 P (RS) = 1 - 0.50 - 0.20 - 0.10           = 0.20 P (P…

Q: Decide if the events A and B are mutually exclusive or not mutually exclusive. A card is drawn from…

A: Mutually exclusive: If two events cannot happen together, then it is called mutually exclusive…

Q: A fair coin is independently flipped n times, k times by A and n -k times by B. Show that the…

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Q: Let S= {a,b,c,d,e} with P(a)= .11, P(b) =.01, P(c)= .06 and P(d)= .08. If F is the event find…

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Q: Consider the set Z = {A, B, C, D}.   Three items are selected from Z with replacement and…

A: Given data set Z={A,B,C,D}

Q: Suppose that A, B are two events such that P(A) > 0 and P(B) > 0.  If A and B are not disjoint, then…

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Q: Prove or disprove. Given n (n > 1) events A. A,. .A, E5, then n PIA]- PIA, N A,] < PIJ4;]< P[A,] i=1

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Q: a Find P(C), P(D), P(C D) and P(CU D). b Hence show that P(CU D) = P(C) + P(D). %3D C State with a…

A: Given: C = { 1 , 3 , 9 , 27 , 81 , 243 , 729} D= { 2 , 4 , 8 , 16 , 32 } n(C) = 7 n(D) = 5  n(S)= 12…

Q: Are the events male cheated and female right independent? Show the computations needed to justify…

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Q: Suppose a coin is flipped until both a head and a tail appear, or until the coin has been flipped…

A: Let us denote H=head, T=tail  The sample space of the given event is= {HT, TH, HHT, TTH, HHHT, TTTH,…

Q: For any two events A and B and P(B) # 1 and A N B = Ø, find weather the following statement is true…

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Q: Event C is defined as the set of positive even integers; Event E is defined as the set of odd…

A: Mutually Exclusive Events: Another name of Mutually exclusive events is Disjoint events. An event is…

Q: Let S = {a, b, c, d, e} with P(a) = 0.29, P(b) = 0.18, P(c) = 0.12, and P(d) = 0.08. If F is the…

A: According to the given information, we have S ={a, b, c, d, e} P(a) = 0.29 P(b) = 0.18 P(c) = 0.12…

Q: Assume that it is equally likely for a child to be born a boy or a girl, and that the Lin family is…

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Q: Suppose that, for events A and B, P(A)= 0.2, P(B)= 0.85, and P(AandB)= 0.17.    Calculate the…

A: Given: Suppose that, for events A and B, P(A)= 0.2, P(B)= 0.85, and P(AandB)= 0.17.    Calculate the…

Q: If A and B are independent events, prove that the following pairs of events are independent: Ac and…

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Q: For any two events A and B, find weather the following statement is true or not: P(ANB) + P(AC N B)…

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Q: If a license number is selected randomly, what is the probability that yours is the one selected?

A: 3 places to be filled with 10 choices for each place: 10*10*10= 10³ = 1000

Q: From a box containing 6 red balls, 8 white balls and 10 blue balls, one ball is drawn at random.…

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Q: b) What is the defn of event Suppose toss two coina. Worite down the names of al the memberes of…

A: From the given information, The event space can be defined as below:

Q: Let A and B be two events such that 0 < P(A) < 1. If P(B|A) = P(B|Ac), prove mathematically (not…

A: Given that A and B be two events such that 0 &lt; P(A) &lt; 1. If P(B|A) = P(B|Ac), We have to prove…

Q: Write True on the blank if the underlined words in the sentence is an event and False if it is not.…

A: An event is an outcome or a set of outcomes of a random experiment. In probability theory, a…

Q: A survey of 300 students in middle school yielded the following information: 100 like to go to the…

A: Givent that H: like to hike and M: like the movies We will make Venn diagram 40 like to go to the…

Q: The Fundamental Counting Principle - If event M can occur in m ways and is followed by event N that…

A: We have to solve question based on The Fundamental Counting Principle

Q: Ем, As a preliminary helper result, show by induction that for events E1, E2,..., EM, M P(E, or E2…

A: For M=1 the result is true as P(E1)=P(E1) For M=2 we have P(E1 or  E2)=P(E1)+P(E2)-P(E1 and E2)…

Q: Determine whether way set of events is mutually exclusive or not.  randomly select a car in the…

A: If the two events do not occur same time then it is called as mutually exclusive events.

Q: Assume that it is equally likely for a child to be born a boy or a girl, and that the Lin family is…

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Q: Determine whether the events are independent. Numbers are written on slips of paper in a hat; one…

A: Independent Events: If the happening of one event is not dependent on the happening of other…

Q: Picture an experiment that observes the # of computers in use at a five-computer lab. Let A, B be…

A: Given Data: A={ 3, 4, 5 } B={ 1, 3 } S={ 1, 2, 3, 4, 5}

Q: You randomly select an integer from 0 to 7 (inclusively) and then randomly select an integer from U…

A: It is given that, the number of digits from 0 to 7 is 8 and the number of digits from 0 to 4 is 5.

Q: For any two events A and B and P(B)± 1 and A N B = Ø, find weather the following statement is true…

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Q: Let E, F, and G be three events. Find expressions for the events so that, of E, F. and G,

A: Here, we are using definitions of union, intersection and complement. For event A, B A∪B- event in…

Q: On a tv quiz show, a contestant is asked to pick an integer at random from the first 100 consecutive…

A: Solution

Q: Let E and F be event such that P(F) = 0.6, P(E|F) = 0. 5 and P(E|F ) = 0. 3 Find P(F|E) =?

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Q: As a preliminary helper result, show by induction that for events E1, E2,...,EM, M P(E, or E, or...…

A: The complete solutions are given below

Q: Let A and B be events such that 0

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Q: Determine whether the events are independent. Numbers are written on slips of paper in a hat; one…

A: Independent events: If the occurrence of event A doesn’t affect the occurrence of event B, then…

Q: Suppose a card is drawn from a standard 52 cards deck. Spades, Diamonds, Clubs, Hearts Let A denote…

A: Two events A and B are said to be independent if; P(A∩B)=P(A)×P(B) Two events A and B are said to be…

Q: A person chooses a single state from all 50 states in the United States. Find the set representing…

A: A person chooses a single state from all 50 states in the United States.

Q: mich of the following pairs of events are independent? Select all that apply. A. Draw a 2 of clubs…

A: as per policy only first three subparts are answered.

Q: A password has to use the following format: LDDDDLLL, where L can be any of the upper case letters…

A: a. The probability that the random password uses only vowels and odd numbers is obtained below: The…

Q: Prove that if A and B are events, then Pr[A] – Pr[B] < Pr[A\ B]

A: LHS =PA-PB=PA-PA∩B In LHS, we are subtracting, therefore, the value of LHS will be small