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Question: The ratings of Monty Hall's show have dropped slightly, and a panicking executive producer complains to Monty that the part of the show where he opens a door lacks suspense: Monty always opens a door with a goat. Monty replies that the reason is so that the game is never spoiled by him revealing the car, but he agrees to update the game as follows. Before each show, Monty secretly flips a coin with probability p of Heads. If the coin lands Heads, Monty resolves to open a goat door (with equal probabilities if there is a choice). Otherwise, Monty resolves to open a random unopened door, with equal probabilities. The contestant knows p but does not know the outcome of the coin flip. When the show starts, the contestant chooses a door. Monty (who knows where the car is) then opens a door. If the car is revealed, the game is over; if a goat is revealed, the contestant is ordered the option of switching. Now suppose it turns out that the contestant opens door 1 and then Monty opens door 2, revealing a goat. What is the contestant's probability of success if he or she switches to door 3?
MATH1550H: Assignment: Question: A word is selected at random from the following poem of Persian poet and mathematician Omar Khayyam (1048-1131), translated by English poet Edward Fitzgerald (1808-1883). Find the expected value of the length of th..
MATH1550H: Assignment: Question: what is the least number of applicants that should be interviewed so as to have at least 50% chance of finding one such secretary?
MATH1550H: Assignment: Question: Experience shows that X, the number of customers entering a post office during any period of time t, is a random variable the probability mass function of which is of the form
MATH1550H: Assignment:Questions: (Genetics) What is the probability that at most two of the offspring are aa?
MATH1550H: Assignment: Questions: Let’s assume the department of Mathematics of Trent University has 11 faculty members. For i = 0; 1; 2; 3; find pi, the probability that i of them were born on Canada Day using the binomial distributions.
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