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

Study concepts, example questions & explanations for ISEE Middle Level Math

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Example Questions

Example Question #51 : Probability

 

 

Find the probability of rolling a multiple of 3 on a dice.

Possible Answers:

Correct answer:

Explanation:

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

 

Now, given the event of rolling a multiple of 3 on a dice, we can determine the following.

because there are 2 multiples of 3 on a dice:

  • 3
  • 6

Now, we can also determine the following:

because there are 6 different numbers we could potentially roll:

  • 1
  • 2
  • 3
  • 4
  • 5
  • 6

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

 

Therefore, the probability of rolling a multiple of 3 on a dice is 

Example Question #551 : Data Analysis And Probability

Find the probability of picking an even number between 1 and 10 (1 and 10 are included).

Possible Answers:

Correct answer:

Explanation:

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

 

Now, given the event of picking an even number between 1 and 10, we can determine the following.

because there are 5 even numbers between 1 and 10:

  • 2
  • 4
  • 6
  • 8
  • 10

Now, we can also determine the following:

because there are 10 different numbers we could potentially pick:

  • 1
  • 2
  • 3
  • 4
  • 5
  • 6
  • 7
  • 8
  • 9
  • 10

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

 

Therefore, the probability of picking an even number between 1 and 10 is .

Example Question #552 : Data Analysis And Probability

Find the probability of rolling a factor of 5 on a dice.

Possible Answers:

Correct answer:

Explanation:

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 .

Example Question #51 : Probability

Find the probability of rolling a multiple of 2 on a dice.

Possible Answers:

Correct answer:

Explanation:

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

 

Now, given the event of rolling a multiple of 2, we can calculate the following.

because there are 3 multiples of 2 on a dice:

  • 2
  • 4
  • 6

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 multiple of 2 on a dice is .

Example Question #52 : How To Find The Probability Of An Outcome

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

Possible Answers:

Correct answer:

Explanation:

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

 

Now, given the event of drawing an Ace from a deck of cards, we can calculate the following.

because there are 4 Aces in a deck of cards that we could draw:

  • Ace of Hearts
  • Ace of Diamonds
  • Ace of Spades
  • Ace of Clubs

Now, we can calculate he following.

because there are 52 total cards within a deck that we could potentially draw. 

 

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

 

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

Example Question #52 : Probability

Find the probability of rolling a factor of 2 on a dice.

Possible Answers:

Correct answer:

Explanation:

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

 

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

 

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

Example Question #54 : How To Find The Probability Of An Outcome

A bag contains the following:

  • 3 blue pens
  • 2 red pens
  • 5 black pens
  • 2 pencils

Find the probability of grabbing a pencil out of the bag.

Possible Answers:

Correct answer:

Explanation:

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

 

Now, given the event of drawing a pencil out of the bag, we can determine the following:

because there are 2 pencils in the bag.

 

Now, we can determine the following:

because there are 12 total objects in the bag we could potentially draw:

  • 3 blue pens
  • 2 red pens
  • 5 black pens
  • 2 pencils

 

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

 

Therefore, the probability of drawing a pencil out of the bag is .

Example Question #561 : Data Analysis And Probability

A classroom contains 8 boys and 12 girls.  

Find the probability the teacher calls on a boy.

Possible Answers:

Correct answer:

Explanation:

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

 

Now, given the event of the teacher calling on a boy, we can determine the following:

because there are 8 boys in the classroom.

 

Now, we can determine the following:

because there are 20 total students in the class the teacher could potentially call on:

  • 8 boys
  • 12 girls

 

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

 

Therefore, the probability of the teacher calling on a boy is .

Example Question #561 : Data Analysis And Probability

A bag contains the following:

  • 5 red pens
  • 3 blue pens
  • 4 black pens

Find the probability of grabbing a blue pen from the bag.

Possible Answers:

Correct answer:

Explanation:

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

 

Now, given the event of grabbing a blue pen from the bag, we can calculate the following:

because there are 3 blue pens in the bag.

 

Now, we can calculate the following:

because there are 12 pens in the bag we could potentially grab:

  • 5 red pens
  • 3 blue pens
  • 4 black pens

 

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

 

Therefore, the probability of grabbing a blue pen from the bag is .

Example Question #562 : Data Analysis And Probability

Find the probability of rolling a factor of 6 on a dice.

Possible Answers:

Correct answer:

Explanation:

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 .

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