coin is tossed (H‚ T). (a) Enumerate the elementary events in the sample space for the die/coin combination. (b) Are the elementary events equally likely? Explain. A) Elementary events are - DIE COIN 1 2 3 4 5 6 HEADS H1 H2 H3 H4 H5 H6 TAILS T1 T2 T3 T4 T5 T6 B) YES‚ EACH EVENT IS EQUALLY LIKELY TO OCCUR. THERE ARE 12 POSSIBLE OUTCOMES AS A RESULT OF ROLLING OE DIE AND FLIPPING ONE COIN‚ THEREFORE THE LIKELYHOOD OF ANY ONE EVENT OCCURING IS 1/12. 5.13 (page 186)‚ 5.13 Given P(A)
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Probability Introduction The probability of a specified event is the chance or likelihood that it will occur. There are several ways of viewing probability. One would be experimental in nature‚ where we repeatedly conduct an experiment. Suppose we flipped a coin over and over and over again and it came up heads about half of the time; we would expect that in the future whenever we flipped the coin it would turn up heads about half of the time. When a weather reporter says “there is a 10% chance
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of the basic rules of probability: the sum of the probability that an event will happen and the probability that the event won’t happen is always 1. (In other words‚ the chance that anything might or might not happen is always 100%). If we can work out the probability that no two people will have the same birthday‚ we can use this rule to find the probability that two people will share a birthday: P(event happens) + P(event doesn’t happen) = 1 P(two people share birthday) + P(no two people share
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13 4. Introduction to Probability ....................................................................... 15 5. Unions‚ Intersections‚ and Complements ................................................ 23 6. Conditional Probability & Independent Events..................................... 28 7. Discrete Random Variables....................................................................... 33 8. Binomial Random Variable ...................................................................... 37
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weights. Then 6 1 ‚...‚m(ω6 ) = 21 . (Check for yourself that this choice of values of m(ωi ) satisfies m(ω1 ) = 21 the three conditions above!) Therefore‚ P (Even) = P ({2‚ 4‚ 6} = 2 21 + 4 21 + 6 21 = 12 21 = 4 7 = 0.57. 7. Let A and B be events such that P (A ∩ B) = 14 ‚ P (Ac ) = 13 ‚ and P (B = 12 . What is P (A ∪ B)? Recall Theorem 4 from class: P (A ∪ B) = P (A) + P (B) − P (A ∩ B). We already know that P (B) = 12 and P (A ∩ B) = 14 ‚ so we just need to find P (A). By Theorem 1 part
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shift requires 6 operators‚ 2 maintenance persons‚ and 1 supervisor‚ in how many different ways can it be staffed? [8 points] 18 10 4 18564 45 4 3‚341‚520 6 2 1 (b) Suppose A and B are not mutually exclusive events‚ and we have P(A)=0.35‚ P(B)=0.40‚ P(AB)=0.18. Compute the following probabilities: i) P (AB)=? [4 points] P (AB)=P[A]+P[B]-P[AB]=0.35+0.40-0.18=0.57 ii) P(AB)=? P[A B] P[ A B] 0.18 0.45 P[ B] 0.40 1 of 6 [4 points] Name: Problem
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input the probabilities of 0.4‚ 0.4 and 0.2 for “good”‚ “moderate” and “poor” market reception. We then proceed to develop the marginal‚ conditional‚ and joint probabilities for each terminal end-point. The formula for the conditional probability of events A and B is changed as: P(A ∩ B) = P(B) P(A | B) By developing the likely revenue of market response outcome and summing the results‚ we obtain the expected
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PROBABILITY QUESTIONS Q1). You draw a card at random from a standard deck of 52 cards. Neither you nor anyone else looked at the card you picked. You keep it face down. Your friend then picks a card at random from a remaining 51 cards. a) What is the probability that your card is ace of spades? 1/52 b) What is the probability that your friend’s card is ace of spades? (Hint: Construct the sample space for what your friend’s card can be.) 1/51 c) You turn over your card and it is 10 of
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Memories are what every human has experienced in the past‚ whether tragic‚ funny‚ shocking‚ and so on. We all have one memory in which it can’t be effaced from our lives. When I ask myself what memory can’t be relinquished from my mind only one comes into my understanding. I can consider my memory out of all the categories that I mentioned funny. The theory that I have developed evaluating this memory‚ I could say that funny memories or memories in general take place when you least expect it. This
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