3 to 2 odds in favor of heads is equal to a probability of , which is the probability that the penny will come up heads. Similarly, 4 to 3 odds in favor of heads is equal to a probability of , which is the probability that the nickel will come up heads. 

Since the tosses of the two coins are independent, multiply the probabilities. The probability that there will be two heads is

This is  to 12 against both coins coming up heads.

5 to 4 odds in favor of heads is equal to a probability of , which is the probability that the penny will come up heads. The probability that the penny will come up tails is .

Similarly, 4 to 3 odds in favor of heads is equal to a probability of , which is the probability that the nickel will come up heads. The probablity that the nickel will come up tails is .

The outcomes of the tosses of the penny and the nickel are independent, so the probabilities can be multiplied.

The probability of the penny being heads and the nickel being tails is ; that of the reverse is .  

These are disjoint, so add these probabilities; the probability that one head and one tail will come up will be . This translates to  to 31 odds against this event.

Each die comes up "1" with probability , and the probabilities of the other five rolls are equal, so the probability of a "2" on either die (or any other roll) is .

The probability of rolling a double 1 is .

The probability of rolling any other given double is .

Therefore, the probability of rolling any ofthe six doubles is 

,

which is  odds against doubles - that is, 40 to 9. 

There are four aces in a standard fifty-two card deck. So we set up a fraction.

 The numerator represents how many possibilites we are looking for. The denominator represents the total in the given data.

Answer is .

When we see the word or, we are adding probabilities. Since we are looking for white or blue, our chance is:

 The numerator represents how many possibilites we are looking for. The denominator represents the total in the given data.

Answer is .

Since I don't want a blue ball, I just subtract the total number of balls and the number of blue balls in the set. The probability is:

 The numerator represents how many possibilites we are looking for. The denominator represents the total in the given data.

Answer is .

Since we are trying to get first black then red balls without replacement, this is a condition we need to meet. This means we need to multiply probabilities. For my first pick I have five balls out of eighteen in which the probability is  . With one ball gone, there are only seventeen balls left. Since I want a red ball next, there are three left out of seventeen balls or . Now, we multiply our probabilities:

. 

Since we are trying to get two apples without replacement, this is a condition we need to meet. This means we need to multiply probabilities. For his first pick he has five apples out of twenty fruits in which the probability is  or . With one apple gone, there are only nineteen fruits left. Since he wants to get another apple, there areonly four apples left out of nineteen fruits or . Now, we multiply our probabilities:

. 

Prime numbers are numbers with factors of  and itself. Those numbers are . Our probability:

 The numerator represents how many possibilites we are looking for. The denominator represents the total in the given data.

Answer is .

To not get any heads, this would mean Sheila would need to get tails on all the flips. Since there are two choices in a flip and Sheila only want tails, our chances is . Since she needs this done twice more, this becomes a condition and we need to multiply out our probabiities. The odds are the same so our answer is just .