When finding the probability of an outcome, we use the following formula:

In this case, the event we are looking at is when the coin lands on tails. When flipping a coin, the number of ways it will land on tails is equal to 1.  There is only 1 side of the coin that displays tails, so only 1 way it can land on tails.

Now, the possible outcomes (or possible results) are

• heads
• tails

So, the total number of possible outcomes is 2.

Therefore, the probability of landing on tails when flipping a coin is

Since the two events have nothing to do with each other, the probability of someone else rolling a  would be  since there are six possible outcomes and you are looking specifically at only one.

To find the probability of something, we use the following formula:

So, if we look at the event of rolling a 3 on a dice, we can see

because on a single dice, there is only one 3. 

Now, if we look at the total number of possible outcomes, we can see

because there are 6 different numbers we can roll:

• 1
• 2
• 3
• 4
• 5
• 6

Knowing this, we can substitute into the formula.  We get

Therefore, the probability of rolling a 3 is .

To find the probability of an event, we will use the following formula:

Now, given the event of flipping a coin and landing on heads, we can determine

because there is only 1 way the coin will land on heads.

Now, we will determine the outcomes.  We know

because there are 2 outcomes when flipping the coin.  They are

• heads
• tails

Now, we can use this information to substitute into the formula.  We get

Therefore, the probability of flipping a coin and it lands on heads is .

To find the probability of an event, we will use the following formula:

Now, given the event of rolling a dice and getting an odd number, we can determine

because there are 3 ways we can get an odd number when rolling a dice:

• 1
• 3
• 5

Now, we will determine the outcomes.  We know

because there are 6 outcomes when rolling the dice.  They are

• 1
• 2
• 3
• 4
• 5
• 6

Now, we can use this information to substitute into the formula.  We get

Now, we can simplify.

Therefore, the probability of rolling a dice and getting an odd number is .

To find the probability of an event, we will use the following formula:

So, if we look at flipping a coin, and it lands on heads, we can see

because there is only 1 heads side on a coin.

If we look at the total number of possible outcomes, we see

because there are 2 different outcomes when flipping a coin:

1. heads
2. tails

Now, using this information, we can substitute into the formula.  We get

Therefore, the probability of getting heads when flipping a coin is .

To find the probability of an event, we will use the following formula:

So, if we look at drawing a green marble, we can see

because there are 4 green marbles in the bag.

If we look at the total number of possible outcomes, we see

because there are 10 total marbles in the bag:

• 1 blue marble
• 4 green marbles
• 2 black marbles
• 3 yellow marbles

Now, using this information, we can substitute into the formula.  We get

Now, we can simplify.  We get

Therefore, the probability of drawing a green marble from the bag is .

Caitlin started with 15 pieces of candy.

Since she already picked one, she is left with 14 pieces.

She already picked a purple candy, so now there are only 2 purple pieces left.

Therefore, she has  chance of picking purple.

This fraction reduced is .

Each flip of the coin is an independent event and the previous flip has no impact on any following flips of the coin.

Therefore, for every coin toss, there is a 50%.

Thus there is a 1/2 chance that the coin will land on heads.

To find the probability of an event, we will use the following formula:

So, we know a classroom has 20 boys and 10 girls.  The question wants to know the probability of calling on a boy.  So, we will first find the number of ways the event can happen.  We get

because there are 20 boys that the teacher could call on.  Now, we will find the total number of possible outcomes.

because there are 30 different students in the classroom that the teacher could call on.

Knowing this, we can substitute into the formula.  We get

Now, we can simplify.  The zero in 20 can cancel the zero in 30.  We get

Therefore, the probability that a teacher calls on a boy is .