A First Course in Probability (10th Edition)

Chapter 3

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. ; Suppose is the event that at least one land ... more

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The table shows the probability for each : ... more

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0.06061. ; Suppose, be the event that North and ... more

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The table shows the probability for each : ... more

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. ; There are 6 white and 9 black balls in the urn... more

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in both of the case. ; Suppose be the event that... more

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. ; The king is male. Suppose denotes girl and ... more

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. ; A couple has 2 children. Suppose, is the ... more

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. ; Suppose that is the event that white ball is ... more

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0.22. ; Suppose that is the event that first card... more

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. ; Suppose that 3 distinct numbers are written on... more

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0.1055. ; The probability can be written as ... more

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. ; The probability of developing Ectopic ... more

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0.98353. ; Suppose event denotes baby survives, ... more

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YesThe probability of B's hanging up phone with a ... more

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Let be the event that a person in the particular ... more

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; Let be the event where the person is ... more

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Second method is better, because in the second ... more

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0.893 ; Consider all the 4 cases, case 1 is where ... more

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; Let be the event where the first box is being ... more

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0.87 ; Let be the event that a certain suspect is... more

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0.5 ; The goal is to find the total number of ... more

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0.32 ; Let B=coin landed tails and A=coin landed ... more

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; Let be the event that the policy holder is ... more

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0.09 ; Let A =ace is drawn from the first deckB= ... more

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0.44 ; Let be the event of choosing the coin ... more

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The probability of A to be executed will not ... more

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The probability that the person is in a specific ... more

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0.075 and 0.04 ; Let A =only white ball is drawn ... more

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0.66 ; Let A= A cabinet is chosenB=B cabinet is ... more

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, and ; Let , , be the events that a person is ... more

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; A being the winner of the tournament can be ... more

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; If atleast one of the component works; system ... more

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9 ; With the present number of boys and girls in ... more

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; Probability of the nth coupon drawn is new  (... more

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0.4375. ; of twins are of same sex and of all ... more

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. ; Let be the event that flow of current is from... more

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.. ; 50 -50 chance that the queen carries the gene... more

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, ; A town council of 7 members contains a ... more

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; When two dices are tossed, the probability of ... more

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 Here, Apply  the probability of  complement and ... more

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0.55 ; Lets following variables denoted the events... more

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0.953  ; Let be the stock goes up by one pointLet... more

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For part (a),For part (b), ; Assume, be the event ... more

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The main aim is to the show that .Let be a set, ... more

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or ; The game can be divided into three stages.... more

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; Assume,  be the event of getting all heads in ... more

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Yes.When a fair coin flips, there are only two ... more

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; Assume, be the event that at least one of the ... more

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As given As, That is , .Now, Now, then, Hence, ; ... more

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; As Then, Hence, ; Now,  ; more

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Let denotes that the selected child is oldest in ... more

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Let be the event that the ball is in box and be... more

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; Follow the below steps using the De-Morgan's ... more

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Now, two events are independent if,   As, all the ... more

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0.155 ; Let :: Event that women as a positive ... more

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; Let denotes the probability of getting at ... more

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The first success is in experiment with ... more

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Let be the event that flips heads before flips... more

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Firstly the restrictions on infinitely rich ... more

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Let be the event that experiments are needed to ... more

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The even number of successes are possible is the ... more

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; Assume, be the probability of not getting ... more

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Assume, be the success probability of winning a ... more

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Assume, be the probability of drawing a white ball... more

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Part 1. Assume, represents the probability of ... more

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Assume, represents the probability of the event ... more

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Assume, be the total number of contestants be an ... more

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Assume, , and be any events, where represents ... more

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Equation 5.11 is given as follows:Equation 5.12 is... more

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The relation for conditional independence of event... more

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The given statement is not true, following is a ... more

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Assume, be the event of first getting heads. be... more

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Assume, be an event of getting number of heads ... more

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In this case, the probability given by the Laplace... more

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5 white and 5 black balls in each urn ; There are ... more

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; \begin{aligned}The\;probability\;that\;ball\;... more

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and ; Let denote the event that first ball drawn... more

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Hypothesis G is more likely after the evidence has... more

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0.5 ; Let denotes that event that the person ... more

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Though getting consecutive 11 black on roulette is... more

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; The probability that is excluded in single ... more

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; To find the probability .As the trials are ... more

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Assume, be the event of getting more heads than ... more

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Assume, and are two with and .If event and ... more

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As the events are independent, the product rule of... more

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; Assume, be the event that the radio is ... more

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is the conditional probability of happening of ... more

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To show that after stages, the probability of ... more

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Assume, and be any two events. and be the ... more

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Assume be any three independent events. If two ... more

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The required probabilities are 0.5 and 0.833 ; Let... more

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Required conditional probability is 0.0893 ; Total... more

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The required probability is 0.15 ; Ei be the ... more

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