Proabability in Scrabble expected number does it take to draw a blank,(yes replacement)
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In the game of Scrabble, players begin by drawing 7 tiles from a bag containing 100 tiles, 2 of which are blank. A player cheats by looking at the first tile he draws, and if it is not blank, he replaces the tile and draws again, repeating this process until he draws a blank tile. What is the expected number of draws this player must make until he draws a blank tile?
statistics
asked Dec 22 '18 at 20:00
helpmehelpme
1
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$begingroup$
In the game of Scrabble, players begin by drawing 7 tiles from a bag containing 100 tiles, 2 of which are blank. A player cheats by looking at the first tile he draws, and if it is not blank, he replaces the tile and draws again, repeating this process until he draws a blank tile. What is the expected number of draws this player must make until he draws a blank tile?
statistics
asked Dec 22 '18 at 20:00
helpmehelpme
1
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add a comment |
$begingroup$
In the game of Scrabble, players begin by drawing 7 tiles from a bag containing 100 tiles, 2 of which are blank. A player cheats by looking at the first tile he draws, and if it is not blank, he replaces the tile and draws again, repeating this process until he draws a blank tile. What is the expected number of draws this player must make until he draws a blank tile?
statistics
asked Dec 22 '18 at 20:00
helpmehelpme
1
$endgroup$
In the game of Scrabble, players begin by drawing 7 tiles from a bag containing 100 tiles, 2 of which are blank. A player cheats by looking at the first tile he draws, and if it is not blank, he replaces the tile and draws again, repeating this process until he draws a blank tile. What is the expected number of draws this player must make until he draws a blank tile?
statistics
statistics
asked Dec 22 '18 at 20:00
helpmehelpme
1
asked Dec 22 '18 at 20:00
helpmehelpme
1
asked Dec 22 '18 at 20:00
helpmehelpme
1
asked Dec 22 '18 at 20:00
helpmehelpme
1
asked Dec 22 '18 at 20:00
helpmehelpme
1
1
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1 Answer
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Let $X$ be the number of draws the player has to make to draw a blank. The probability that any given draw is a success is $frac{1}{50}$ and we continue until we succeed so $X$ is geometrically distributed with parameter $frac{1}{50}$.
The expected value of a geometrically distributed random variable with probability $p$ is $frac{1}{p}$, so in your case, the expected number of draws the player must make is $50$.
answered Dec 22 '18 at 20:05
ODFODF
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1 Answer
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$begingroup$
Let $X$ be the number of draws the player has to make to draw a blank. The probability that any given draw is a success is $frac{1}{50}$ and we continue until we succeed so $X$ is geometrically distributed with parameter $frac{1}{50}$.
The expected value of a geometrically distributed random variable with probability $p$ is $frac{1}{p}$, so in your case, the expected number of draws the player must make is $50$.
answered Dec 22 '18 at 20:05
ODFODF
1,484510
$endgroup$
add a comment |
$begingroup$
Let $X$ be the number of draws the player has to make to draw a blank. The probability that any given draw is a success is $frac{1}{50}$ and we continue until we succeed so $X$ is geometrically distributed with parameter $frac{1}{50}$.
The expected value of a geometrically distributed random variable with probability $p$ is $frac{1}{p}$, so in your case, the expected number of draws the player must make is $50$.
answered Dec 22 '18 at 20:05
ODFODF
1,484510
$endgroup$
add a comment |
$begingroup$
Let $X$ be the number of draws the player has to make to draw a blank. The probability that any given draw is a success is $frac{1}{50}$ and we continue until we succeed so $X$ is geometrically distributed with parameter $frac{1}{50}$.
The expected value of a geometrically distributed random variable with probability $p$ is $frac{1}{p}$, so in your case, the expected number of draws the player must make is $50$.
answered Dec 22 '18 at 20:05
ODFODF
1,484510
$endgroup$
Let $X$ be the number of draws the player has to make to draw a blank. The probability that any given draw is a success is $frac{1}{50}$ and we continue until we succeed so $X$ is geometrically distributed with parameter $frac{1}{50}$.
The expected value of a geometrically distributed random variable with probability $p$ is $frac{1}{p}$, so in your case, the expected number of draws the player must make is $50$.
answered Dec 22 '18 at 20:05
ODFODF
1,484510
answered Dec 22 '18 at 20:05
ODFODF
1,484510
answered Dec 22 '18 at 20:05
ODFODF
1,484510
answered Dec 22 '18 at 20:05
ODFODF
1,484510
1,484510
add a comment |
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