# ISEE Middle Level Math : How to find the probability of an outcome

## Example Questions

### Example Question #31 : Develop And Compare Probability Models And Find Probabilities Of Events: Ccss.Math.Content.7.Sp.C.7

A pair of fair six-sided dice are thrown, and the sum of the numbers facing upward is noted. What is the probability that a sum of 8 or 9 will be thrown?

Explanation:

There are   possible rolls of two fair six-sided dice, each of which will come up with equal probability. The set of rolls is shown below, with the ways to roll a sum of 8 or 9 indicated.

There are 9 ways out of 36 to roll a sum of 8 or 9, making the probability of this outcome .

### Example Question #31 : Outcomes

What is the probability of drawing a 10 from a deck of cards?

Explanation:

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

So, if we look at the event of drawing a 10 from a deck of cards, we can determine the following:

because there are 4 ways we can draw a 10:

• 10 of hearts
• 10 of diamonds
• 10 of clubs

because there are 52 total cards to choose from.

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

Now, we simplify.

Therefore, the probability of drawing a 10 from a deck of cards is .

### Example Question #31 : Probability

If you have  students on a bus which includes  seniors, how many freshmen are riding if the remaining students are equally likely to be freshmen, sophomores, or juniors?

Explanation:

The first step is to take the seniors out of the equation

.

With  students left over, you divide that number by three since each of the three remaining groups are equally likely.

This gives you a final answer of .

### Example Question #31 : Probability

people attend a concert and  of them are males.  What probability is there of selecting a random guest and them being female?

Explanation:

Since there are  males at the concert, that means there are  women

.

To find the probability of selecting a woman, you divide the number of women by the total number of quests giving you

.

### Example Question #541 : Data Analysis And Probability

Find the probability of drawing a 2 from a deck of cards.

Explanation:

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

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 .

### Example Question #31 : How To Find The Probability Of An Outcome

Find the probability of drawing an Ace of spades from a deck of cards.

Explanation:

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

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

because there is only 1 Ace of spades in a deck of cards.

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.

Therefore, the probability of drawing an Ace of spades from a deck of cards is .

### Example Question #35 : Probability

Find the probability of drawing a King from a deck of cards.

Explanation:

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

So, given the event of drawing a King from a deck of cards, we can see

because there are 4 Kings in a deck of cards:

1. King of Hearts
2. King of Diamonds
3. King of Clubs

Now, we will look at total outcomes.  We get

because there are 52 cards in a deck (in other words 52 different possibilities when drawing a card).

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

Now, we simplify.

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

### Example Question #542 : Data Analysis And Probability

Find the probability of drawing a 7 of Diamonds from a deck of cards.

Explanation:

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

So, given the event of drawing a 7 of Diamonds from a deck of cards, we can see

because there is only 1 7 of Diamonds in a deck of cards.

Now, we will look at total outcomes.  We get

because there are 52 cards in a deck (in other words 52 different possibilities when drawing a card).

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

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

### Example Question #101 : Statistics & Probability

A large box contains some balls, each marked with a whole number from "1" to "10". Each number is represented by one red ball. In addition, each prime number is represented by one green ball, and each composite number is represented by one blue ball.

Give the probability that a randomly-drawn ball will be green.

Explanation:

Each number will be represented by one red ball, so there will be ten red balls in the box.

The prime numbers - the numbers that have only 1 and themselves as factors - are 2, 3, 5, and 7, so there will be four green balls.

The composite numbers - the numbers that have more than two factors - are 4, 6, 8, 9, and 10, so there will be five blue balls.

Note that 1 is neither prime nor composite.

The total number of balls is , four of which are green, so the probability of drawing a green ball at random is .

### Example Question #41 : Develop And Compare Probability Models And Find Probabilities Of Events: Ccss.Math.Content.7.Sp.C.7

A large box contains some balls, each marked with a whole number from "1" to "10". Each odd number is represented by one ball, which is red; each even number is represented by two balls, one red and one green.

Give the probability that a randomly-drawn ball will be red.