ISEE Middle Level Math : Probability

Example Questions

Example Question #1 : Approximate The Probability Of A Chance Event By Collecting Data: Ccss.Math.Content.7.Sp.C.6

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?

Explanation:

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 : How To Find The Probability Of An Outcome

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 : Probability

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 : How To Find The Probability Of An Outcome

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

Explanation:

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

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 #34 : How To Find The Probability Of An Outcome

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 #35 : 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?

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 #31 : Outcomes

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 #33 : Probability

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 #34 : 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 #35 : 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 .