Let's list all possible outcomes.

We have H T, H, H, T T, T H.

There are four possible outcomes so that represents the denominator.

Since we are looking for two tails, we only have one possible outcome which is the numerator.

Our final answer is 

. 

There are three face cards which are J Q K.

Next, there are four suits for every face card which gives us a total of  cards we are looking for.

Finally, since there are  cards in a deck, we do a fraction of .

There is no answer given however if we divide top and bottom by  we get an answer of 

.

In a die, there are six sides numbered 

.

Prime numbers are numbers with a factor of one and itself.

The prime numbers are .

We have three outcomes and it's divided over six possible outcomes.

So our fraction is  or . 

In a standard deck, there are thirteen kind of cards from . There are four suits. To have a pair is to have the same kind of card but with different suit. Since we are looking for any pair, the first card Bob picks is anything so the probability is .

Because he keeps the card, we have  cards remaining. To get that same card, there are only  of them left in the deck. So the chance of getting a pair becomes .

We don't have this choice but if we divide both sides by  we get .

When we see or, we must add probabilities. Since there are  socks and we are interested in blue or yellow, we add those totals up.

There are  blue or yellow socks to get.

Our fraction now becomes 

.

To draw an ace first, our chances are  or .

Since there is no replacement, we now have  cards.

To draw the three, our chances are .

Because it's two conditions that need to be satisfied, we multiply 

.  

The probability of getting a question right is .

The probability of getting a question wrong is .

We are tempted to multiply both fractions to get an answer of . The issue is we don't know which question needs to be right.

So in this case, we multiply that fraction by  to get an answer of .

If probability of raining is , that means the probability of not raining is .

Probability must add up to  because we are certain of all possible events which are raining and not raining.

By doing the math, our answer is 

.

The probability of picking any letter is .

The question doesn't specify an order as there are two ways of picking .

We can have  first then  or we can have  first, then .

So probability of picking  in no order is 

. 

If A and B are two independent events (the outcome of one does not affect the outcome of the other), the following formula is used to calculate the overall probability.

The event of flipping a coin and rolling a die are independent events since flipping a coin does not affect the probability of rolling a certain number on the die, and vice versa.

The probability of flipping a heads on a coin is .

The probability of rolling a factor of 6 on a six-sided die (1,2,3,6) is .