Question

In the game of Scrabble, each player begins by randomly selecting 7 tiles from a bag containing 100 tiles. There are 42 vowels. 6 consonants, and 2 blank tiles in the bag. Cait chooses her 7 tiles and is surprised to discover that all of them are vowels.

Suppose we performed a simulation to determine the probability that a player will randomly select 7 vowels and in 2 of the 1000 trials of the simulation, all 7 tiles were vowels.

Does this give convincing evidence that Cait's bag of tiles was not well mixed?

A) Yes, because if the bag was well mixed. there is about a 0.2% In the game of Scrabble, each player begins by randomly selecting 7 tiles from a bag containing 100 tiles. There are 42 vowels. 6 consonants, and 2 blank tiles in the bag. Cait chooses her 7 tiles and is surprised to discover that all of them are of getting 7 tiles that are all vowels. Because it is very unlikely for this to happen by chance alone, we have reason to believe that the hag of tiles was not well mixed.

B) No, every player draws tiles randomly in Scrabble, so Cait could have just had bad luck.

C) No, because if the bag was well mixed, there is about a 0.2% chance of getting 7 tiles that are all vowels. Because this is a very unlikely event, we have reason to believe that it could be due to chance.

D) No, because if the bag was well mixed there is about a 0.2% chance of getting 7 tiles that are all vowels. That means that it could happen. 0.0002<0.

E) No, because if the bag was well mixed there is about a 2/7 = 28.6% chance of getting 7 tiles that are all vowels. This is not unlikely.

Answer 1

The probability obtained from the simulation provides convincing evidence that Cait's bag of tiles was not well mixed.

The correct answer is option is A).

Step-by-step explanation:

The probability that a player will randomly select 7 vowels in the game of Scrabble can be calculated by dividing the number of ways to select 7 vowels from the bag by the total number of ways to select 7 tiles from the bag. The group of interest in this case is selecting 7 vowels, the size of the group of interest is 1 (since we're only interested in the specific case of all 7 tiles being vowels), and the size of the sample is 1000 (the number of trials performed in the simulation).

To determine if Cait's bag of tiles was well mixed, we need to compare the probability obtained from the simulation to the expected probability if the bag was well mixed. Option A) states that there is about a 0.2% chance of getting 7 tiles that are all vowels if the bag was well mixed. Since the probability obtained from the simulation is much smaller than the expected probability, it provides convincing evidence that Cait's bag of tiles was not well mixed. Therefore, the correct option is A).