22 out of the 54 students are boys, so 32 are girls. Also, since the boys and the girls are split evenly between the home rooms, each home room has 11 boys and 16 girls for a total of 27 students. 

This means that the probability of a randomly selected student from Mr. Brooks's home room being a girl is ; the probability is the same for Mrs. Kelly's homeroom. By the multiplication principle, the probability of both students being girls is . 

Three whole numbers have an odd product if and only if all three factors are odd. Therefore, for three dice to show an odd product, all three dice must show odd numbers.

The probability of a die showing an odd number is , so the probability of all three dice showing odd numbers - equivalently, the probability of an odd product - is . This translates to

 or 7 to 1 odds against an odd product.

There are  outcomes for the roll of three six-sided dice. Of these outcomes, the following are the ways to roll a 16 or greater:

This is 10 rolls with the desired outcome out of a possible 216, which translates to a probability of 

Two whole numbers have an odd product if and only if both factors are odd. 

After the aces and face cards are removed from each deck, there are nine ranks left - the twos through tens - each of which are represented by four cards and each of which are therefore equally probable in each deck. The probability of drawing an odd card from the red deck is , and the same holds for the blue deck. The probability of drawing two odd cards  - equivalently, the probability of an odd product - is ; this translates to 

 or 65 to 16 odds against this occurrence. This answer is not among the responses.

18 out of the 50 students are boys, so 32 are girls. Also, since the boys and the girls are split evenly between the home rooms, each home room has 9 boys and 16 girls for a total of 25 students. 

This means that the probability of a randomly selected student from Mr. Jones's home room being a boy is , and that of the student being a girl is . These probabilities are the same for Mrs. Wilson's class.

Therefore, the probability of one boy being selected from Mr. Jones's class and one girl being selected from Mrs. Wilson's class is ; the probability of the reverse event is the same. Therefore, the probability of one boy and one girl being selected is 

The odds against this happening are  - that is, 337 to 288.

The only possible combination to roll a sum of 3 is by rolling three 1s.  The probability of rolling any side of a die is .

The odds of rolling three 1s are:

Therefore, the probability of NOT rolling three 1s is:

Each flip of the coin is an independent event, and does not affect the other flips; all that matters is that the coin is fair. Because of that fact, the probability that the tenth flip comes up heads is .

This can more easily be solved by finding the probability that neither will be green, then subtracting it from 1.

The probability that the first ball will be not be green is five out of ten, or .

This will leave nine balls, four not green, making the probability that the second ball will then not be green .

Multiply these probabilities:

This is the probability that neither ball is green; subtract this from 1: 

The die is fair, making each box equally likely to be chosen; also, each marble is equally likely to be chosen after the box is chosen. This makes each marble overall equally likely to be chosen. Since there are 

red marbles out of

marbles total, the probability of choosing a red marble is

The die is fair, making each box equally likely to be chosen; also, each marble is equally likely to be chosen after the box is chosen. This makes each marble overall equally likely to be chosen. Since there are 

white marbles out of

marbles total, the probability of choosing a white marble is