PART C PLEASE (In detail, as I don\'t understand the how and why of any of this
ID: 3299407 • Letter: P
Question
PART C PLEASE (In detail, as I don't understand the how and why of any of this stuff)
An urn contains 10 red and 10 white balls. The balls are drawn from the urn at random, one at a time. Find the probabilities that the fourth white ball is the fourth, fifth, sixth, or seventh ball drawn if the sampling is done
(a) With replacement. (b) Without replacement.
(c) In the World Series, the American League (red) and National League (white) teams play until one team wins four games. Do you think that the urn model pre- sented in this exercise could be used to describe the probabilities of a 4-, 5-, 6-, or 7-game series? (Note that either “red” or “white” could win.) If your answer is yes, would you choose sampling with or without replacement in your model? (For your information, the numbers of 4-, 5-, 6-, and 7-game series, up to and including 2012, were 21, 24, 23, 36. This ignores games that ended in a tie, which occurred in 1907, 1912, and 1922. Also, it does not include the 1903 and 1919–1921 series, in which the winner had to take five out of nine games. The World Series was canceled in 1994.)
Explanation / Answer
c) yes ,because
we can assign Win for any colour ball
and loss for another
the moment when any colour ball reaches 4 , the game is over
with replacement
since the probability of win/loss does not change with time
we will choose sampling with replacement
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