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In the game of Scrabble, each player begins by drawing 7 tiles from a bag containing 100 tiles. There are 42 vowels, 56 consonants, and 2 blank tiles in the bag. Cait chooses her 7 tiles and is surprised to discover that all of them are vowels. Can we use a binomial distribution to approximate this probability?

Sagot :

Considering the hypergeometric variable, it is found that since the population size is less than 20 times the sample size, the binomial distribution cannot be used.

The tiles are chosen without replacement, hence, the hypergeometric distribution is used.

  • The population is composed by the 100 tiles.
  • The sample is composed by 7 tiles.

The hypergeometric distribution can be approximated to the binomial if the population size is at least 20 times the sample size.

[tex]\frac{100}{7} = 14.28 < 20[/tex]

Hence, the binomial distribution cannot be used.

A similar problem is given at https://brainly.com/question/25743676

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