In the game of SCRABBLE, you select letters from the group in the pot that are not already on the board or in your hand or someone else’s. This would be sampling letters without replacement. Suppose that instead of doing this, you select a letter from the pot, write it down, and then return it to the pot. In other words, suppose you sample letters with replacement. Every time you select a new letter, you write it down next to the letter you drew previously. Because you are sampling the pot with replacement, each draw of a letter is an independent event such that the Multiplication Rule for Independent Events applies. (a) Select a letter, write it down, and return the letter to the pot. Do this three times.

When you reach into the pot to select your letters, your result is based on a simulation. In a simulation, random events are modeled in such a way that the simulated outcomes closely match real-world outcomes. In this simulation, your result is simulated based on the frequency distribution of SCRABBLE letters. (Note: Because the results of this experiment are based on a random simulation, Aplia is not responsible for any inappropriate words that may result.)

Before selecting your tiles, what is the probability that your selection (in order) spells the word "axe" (without the use of the blank tile as a wild card)? Give your answer to six decimal places.

b. Repeat your experiment, but this time select, write, and return the letter four times. Again, your results will be generated based on the frequency distribution. Before you select your tiles, what is the probability that the four letters you write down (in order) will spell "zits" (without the use of a blank tile as a wild card)? Give your answer to eight decimal places.