Scrabble In the game of Scrabble, each player begins by drawing 7 tiles from a bag containing 100 files. There are 42 vowels, 56 consonants, and 2 blank tiles in the bag. Chait chooses her 7 tiles and is surprised to discover that all of them are vowels. We can use a simulation to see if this result is likely to happen

by chance.

(a) State the question of interest using the language of probability.

(b) How would you use random digits to imitate one repetition of the process? What variable would you measure?

(c) Use the line of random digits below to perform one repetition. Copy these digits onto your paper. Mark directly on or above them to show how you

determined the outcomes of the change process. 00694 05977 19664 65441 20903 62371 22725 53340

(d) In 1000 repetitions of the simulation, there were 2 times when all 7 tiles were vowels. What conclusion would you draw?

Each player in the game of Scrabble begins by drawing $7$ tiles from a bag of $100$ tiles. The bag contains $42$ vowels, $56$ consonants, and two blank tiles.

We can't foresee the outcomes of a chance process, yet they have a regular distribution over a large number of repetitions. According to the law of large numbers, the fraction of times a specific event occurs in numerous repetitions approaches a single number. The likelihood of a chance outcome is its long-run relative frequency. A probability is a number between $0$ (never happens) and $1$ (happens frequently) (always occurs).

Looking at the question, the following is the question of interest expressed in probability language: When you select exactly $7$ tiles from a bag containing $42$ vowels out of $100$ tiles, what is the likelihood of getting $7$ vowels? This is the question expressed in probabilistic terms.

To duplicate one repetition of the procedure using random digits, we shall proceed as follows: Use numbers with two digits. The tile has a vowel if the number is between $00$ and $41$ The tile is not a vowel if the number is between $42$ and $99$ Choose$7$ random two-digit numbers at random, with no replacements, to avoid number duplication. Then, among the $7$ numbers/tiles, tally how many vowels you have. As a result, the number of vowels is the variable being measured.

The random digits are: $00694,05977,19664,65441,20903,62371,22725,53340$

as indicated in the question. Choose the number's first two digits. It is a vowel if the number is between $00$ and $41$ else, it is not a vowel. Multiple occurrences of a number should be ignored. This is how it's explained:

As a consequence, the following vowels were chosen $00,40,19$

If the number is between $00$ and $41$ we know the tile contains a vowel. If the number is between $42$ and $99$, the $7$ tile is not a vowel. When all tiles were vowels, $1000$ repetitions were issued twice: $\frac{2}{1000}=0.000.2\%$ Because the percentage is less than$5\%$ drawing$7$ vowels is implausible. As a result, we've arrived at a decision.