The probability (p) is equal to the number of a specific event (purple marbles) divided by the total number of events. The probability of NOT p (called q) is equal to In this example:

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

Now, given the event of rolling a factor of 5, we can calculate the following.

because there are 2 factors of 5 on a dice:

• 1
• 5

We can also calculate the following.

because there are 6 different possible numbers we can roll on a dice:

• 1
• 2
• 3
• 4
• 5
• 6

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

Therefore, the probability of rolling a factor of 5 on a dice is .

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

So, in the event of rolling a factor of 4 on a dice, we can determine the number of times that event can happen. So,

because there are 3 factors of 4 on a dice:

• 1
• 2
• 4

Now, we can determine the total number of possible outcomes. We get

because there are 6 different outcomes we can get when rolling the dice:

• 1
• 2
• 3
• 4
• 5
• 6

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

and we simplify.

Therefore, the probability of rolling a factor of 4 on a dice is .

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

So, given the event of drawing a 3 from a deck of cards, we can calculate the following:

Beause there are four 3s we could draw from a deck of cards

• 3 of hearts
• 3 of diamonds
• 3 of clubs
• 3 of spades

Now we can calculate the following:

Because there are 52 cards in the deck we could potentially draw.

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

The rolls that yield a product between and inclusive are:

Therefore there are rolls that fit our criteria out of a total of possible rolls, so the probability of this outcome is .

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

Now, given the event of rolling a factor of 6 on a dice, we can calculate the following:

because there are 4 factors of 6 on a dice:

• 1
• 2
• 3
• 6

Now, we can calculate the following:

because there are 6 possible outcomes we could potentially get when rolling a dice:

• 1
• 2
• 3
• 4
• 5
• 6

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

Therefore, the probability of rolling a factor of 6 on a dice is .

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

Now, given the event of rolling a factor of 2 on a dice, we can calculate the following.

because there are 2 factors of 2 on a dice:

• 1
• 2

Now, we can calculate he following.

because there are 6 possible numbers we could potentially roll on a dice:

• 1
• 2
• 3
• 4
• 5
• 6

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

Therefore, the probability of rolling a factor of 2 on a dice is .

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

Now, given the event of grabbing a red crayon from the box, we can calculate:

because there are 4 red crayons in the box we could grab.

We can also calculate:

because there are 17 total crayons we could potentially grab:

• 9 blue crayons
• 3 green crayons
• 4 red crayons
• 1 yellow crayon

So, we get

Therefore, the probability of grabbing a red crayon from the box is .

There are 13 yellow and red pebbles. There are 25 pebbles total. Therefor the probability of choosing a red or yellow pebble is .

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

Now, we are asked to find the probability of drawing a 2 from a deck of cards. Given that event, we can determine

because there are 4 ways to draw a 2 from a deck of cards:

• 2 of hearts
• 2 of diamonds
• 2 of clubs
• 2 of spades

Now, we can determine the total number of possible outcomes

because there are 52 different cards to choose from.

Knowing this, we can substitute into the formula.

Now, we can simplify.

Therefore, the probability of drawing a 2 from a deck of cards is .