First calculate the number of students:

The percentage of seniors that do not attend honors classes is:

Therefore, the probability of selecting a student who is a senior and one who does not attend honors classes is:

Each toss and roll of the dice are independent events.  The probability of rolling either a head or tail on the first and second trial is one-half.

The probability of rolling any number on the dice is  since there is one number on each of the six faces of the dice.

Multiply all the probabilities.

Adding the joker and the four aces to a 53-card deck will yield a deck of 58 cards, which contains 8 aces and 50 other cards. The odds against drawing an ace at random are therefore  - that is, 25 to 4.

Before the addition of the hearts, the deck had 4 jacks and 48 other cards. The thirteen hearts from the other deck include 1 jack and 12 other cards, so the altered deck contains 5 jacks and 60 other cards. That makes the odds against drawing a jack at random 

 - that is, 12 to 1, just as in the unaltered deck.

Before the addition of the jacks, the deck had 13 clubs and 39 other cards. The 4 jacks from the other deck include 1 club and 3 other cards, so the altered deck contains 14 jacks and 42 other cards. That makes the odds against drawing a club at random 

 - that is, 3 to 1, just as in the unaltered deck

In an unaltered deck, 4 of the 52 cards, or  of the cards, are kings. We are looking for an action that preserves this ratio. 

We see that if the clubs from another deck are added, then there are 5 kings (the 4 original kings plus an added king) and 65 cards total (the original 53 plus the 13 added clubs). 5 of the 65 cards, or  of the cards, are kings, thereby preserving the ratio. 

Of the other choices, none of them change the number of kings in the deck, but all change the total number of cards. Therefore, the ratio of kings to total cards must change. 

Adding the four sevens from another deck to a 53-card deck will yield a 57-card deck with 14 hearts - the original 13 hearts and the added seven of hearts - and 43 other cards. Therefore, the odds against drawing a heart will be 43 to 14.

In an unaltered deck, 13 of the 52 cards, or  of the cards, are spades. We are looking for an action that preserves this ratio. 

If the red fours and the black fives, including the five of spades, are removed, then there are 12 spades left out of 48 cards, which means that  of the cards are spades. This is the correct choice.

Of the other choices, none of them change the number of spades in the deck, but all change the total number of cards. Therefore, the ratio of spades to total cards must change.

Consider first all of the possible ways the men may be arranged, which is

Now, consider all of the ways that Aaron and Gary could be seated beside each other; it may be easier to visualize by drawing it out:

1. A G _ _
2. G A _ _
3. _ A G _
4. _ G A _
5. _ _ A G
6. _ _ G A

As seen, there are six possibilities.

Finally, for each of these cases, Craige and Boone could be seated in one of two ways.

So the probability that Aaron and Gary will be seated beside each other is:

Out of the 100 tiles, there are nine "A" tiles, twelve "E" tiles, nine "I" tiles, eight "O" tiles, and four "U" tiles. This is a total of 

tiles out of 100. 

This makes the probability of drawing one of these tiles