please help on this word problem? because i am kind of confused?
Posted by admin in Uncategorized on 05 25th, 2010 | 2 responses
A roulette wheel has 38 slots, of which 18 are black, 18 are red and 2 are green. When the wheel is spun, the ball is equally likely to come to rest in any of the slots. One of the simplest wagers choose red or black. A bet of $1 on red returns $2 if the ball lands in red slot. Otherwise, the player loses his dollar. When gamblers bet on red or black, the two green slots belong to the house. Because the probability of winning $2 is 18/38, the mean payoff from a $1 bet is twice 18/38, or 94.7 cents. Explain what the law of large numbers tells us about what will happen if a gambler makes very many bets on red.
(please help, because i am kind of confused for points)
2 Comments »
RSS feed for comments on this post. TrackBack URL
The law of large numbers says that the gambler will slowly, but eventually lose all his money since $1 nets a mean of 94.7 cents
The mean payoff from a $1 bet is $0.947 means that the long-run average for each bet is that you lose $0.053, or 5.3 cents. The law of large numbers says that in the long run you will lose a total of 5.3 cents times the number of bets placed. So if you play red 1000 times, you could expect, at the end of the 1000 spins of the wheel, to have lost 1000 times $0.053 = $53.