The 5 th slot has a mark since anton leaves the stop

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√, … , xxxx√ }. The 5 th slot has a √ mark since Anton leaves the stop in this slot. Therefore there is only one possibility for the 5 th slot. In the other Slot #1 Slot #2 - x
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4 slots, we either have “x” or “ - ”. Therefore there are two possibilities for each one of the 4 slots. The total number of possibilities is then 2 4 x 1 = 16. e) Reasoning as in part d, there should be (k-1) busses arriving in the first (n-1) time slots, Anton does not board the first (k-1) busses. P{Anton not boarding (k-1) busses in the first (n-1) stops }= ) ( ) ( ) 1 ( ) 1 ( 1 1 1 k n bus k board bus n k q q p then P { Anton boarding the k th bus in the n th slot} = board bus k n bus k board bus n k p p q q p ) ( 1 1 1 ) ( ) ( f) 1 1 1 0 ) 1 ( 1 ) 1 ( ) ( ) ( ) ( } slot 1)th - (n of end after the just waiting still P{Anton n board bus n bus board bus n k k n bus k board bus n k p p q q p q q p
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Q.3 (20 pts) A senior level engineering student asked his supervisor for a letter of recommendation for a new job. He estimates that there is an 80% chance that he will get the job if he receives a strong recommendation, 40% chance is he receives a moderately good recommendation and 10% chance if he receives a weak recommendation. He further estimates that the probabilities that the recommendation will be strong, moderate or weak are 0.7, 0.2 and 0.1, respectively. a) What is the probability that he will receive a new job offer? b) Given that he does not receive the job offer. What is the probability that he received a moderate recommendation? Solution : S: strong evaluation M: moderate evaluation W: Weak evaluation J: Receive the job offer We are given P (S)=0.7, P(M)=0.2, P(W)=0.1 and P(J|S)=0.8, P(J|M)=0.4, P(J|W)=0.1 a) P(J)= P(J|S)P(S)+ P(J|M)P(M)+ P(J|W)P(W)=0. 6 5 b) 34 . 0 35 . 0 2 . 0 6 . 0 ) ( ) ( ) | ( ) | J P M P M J P J M P
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EE 230 MT1 SOLUTIONS Q.1 (20 pts) A box contains 5 balls numbered 1 to 5. A ball is drawn from the box at random and its number is observed. (Use formal mathematical notation in your answers!) a) What is the sample space of this experiment ? b) Provid e the definition of “outcome” and give an example from the random experiment defined in this question. c) Provide the definition of “event” and give an example. d) Write down the event that the outcome is smaller than or equal to ( ) 2. e)Write down the event that the outcome is greater than or equal to ( ) 5. a. } 5 , 4 , 3 , 2 , 1 { b. Outcome is the result observed at the end of one trial of a random experiment. Any element of the sample space is an outcome. Ex: 1 is an outcome. c. Any subset of the sample space is called an event. Ex: {} }, 3 , 2 , 1 { }, 5 , 4 , 3 , 2 , 1 { d. } 2 , 1 { e. } 5 {
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Q.2 (20 pts) Box-A contains 3 white and 7 red indistinguishable balls.
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