### All ISEE Middle Level Math Resources

## Example Questions

### Example Question #31 : Probability

A *loaded* coin is tossed times, with the result being heads times. Based on this observation, what is the probability that the next toss of this coin will be tails?

**Possible Answers:**

**Correct answer:**

The probability of an event based on observation (empirical probability) can be calculated by dividing the number of times the event occurs by the number of trials total. Since there were trials and heads, there were tails.

The probability of tails is therefore given by the number of tails divided by the total number of trials. Both terms are divisible by , allowing us to simplify the fraction.

### Example Question #31 : Outcomes

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?

**Possible Answers:**

**Correct answer:**

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 #32 : Outcomes

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

**Possible Answers:**

**Correct answer:**

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
- 10 of spades

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 #541 : Data Analysis And Probability

What is the probability of rolling an even number on a dice?

**Possible Answers:**

**Correct answer:**

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

So, if we look at the event of rolling an even number on a dice, we can determine the following:

because there are 3 ways we can roll an even number on a dice:

- 2
- 4
- 6

because there are 6 possible numbers we can roll:

- 1
- 2
- 3
- 4
- 5
- 6

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

Now, we simplify.

Therefore, the probability of rolling an even number on a dice is .

### Example Question #32 : 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?

**Possible Answers:**

**Correct answer:**

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 #32 : How To Find The Probability Of An Outcome

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

**Possible Answers:**

**Correct answer:**

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 #31 : Probability

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

**Possible Answers:**

**Correct answer:**

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 .

### Example Question #31 : Outcomes

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

**Possible Answers:**

**Correct answer:**

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 #541 : Data Analysis And Probability

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

**Possible Answers:**

**Correct answer:**

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:

- King of Hearts
- King of Diamonds
- King of Clubs
- King of Spades

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 #32 : Outcomes

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

**Possible Answers:**

**Correct answer:**

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 .