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Problem: Plain old Monty Hall (a) Make sure you understand why it is always better to switch in the Monty Hall problem described in class. Think about the problem from different angles. Keep it active in your mind for some time. (b) Here's a convincing argument in favor of switching. We can simulate the game. 1. c ← 0 (this counts the number of wins) 2. n ← 0 (this counts the number of trials) 3. place the prize uniformly at random in one of the boxes, call this box x 4. choose a box uniformly at random, call this box y 5. decide that you will not switch no matter what (the simulation of the remainder of the game becomes irrelevant) 6. if x = y then c ← c + 1 7. n ← n + 1 8. print c/n 9. goto 3 It should be obvious that c/n will converge to 1/3 (why?), which is the prob- ability of winning if we adopt a no switch strategy. The simulation works the same way regardless of the actions taken by the host. Did we just prove that there is always a benefit in switching? (something to think about) Assume that Monty Hall does not know where the prize is. He will simply open one of the remaining boxes at random with equal probability. Consider the case where an empty box is revealed. Show that there is no benefit in switching. (d) How can we resolve the inconsistency between (b) and (c)?
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odds ratio odds ratio or is sometimes reported instead of relative risk. this normally gives the odds or likelihood of
Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put 53 tons of coal into each car. The actual weights of coal loaded into each car are normally ..
1 a find the probability of drawing a diamond card in each of the consecutive draws from a wellshuffled pack of cards
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In a lottery game, you pick one number from 000 to 999. If you pick one such number what is the probability that you will win the lottery?
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The Glass Slipper restaurant has operated in a resort community
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Find the probability that there are exactly 2 prescriptions for this drug in a given week and find the probability that there are no more than 5 prescriptions for this drug in a given week.
Raftelis financial consulting reported that the mean quartely water bill in the US is 47.50. Some water systems are operated b public utilities while other water systems are operated by private companies.
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