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 #21 : Outcomes

If Janet rolls a pair of six-sided dice, what is the probability that the dice will come up as snake eyes (meaning that both dice show one dot)?

Possible Answers:

Correct answer:

Explanation:

Given that there are six values that a die may show when rolled, there is a  chance that either dice will show a value of 1. Thus, the chance that both dice will show a value of 1 is equal to , which is equal to .

Thus,  is the correct answer. 

Example Question #21 : How To Find The Probability Of An Outcome

The probability of getting a heads on a coin toss changes depending on what the previous toss was. True or false?

Possible Answers:

True

False

Correct answer:

False

Explanation:

Since a coin toss is an independent event (no other events affect its outcomes), the probability of getting a heads on a toss will always be .

Example Question #82 : Statistics & Probability

What is the probability of drawing a card that is a spade from a deck of cards?

Possible Answers:

Correct answer:

Explanation:

There are  cards in a deck.  

There are four suits of cards including spades.  

They make up an even amount of the deck each.  

Since there are four of the suits, each represent  of the deck and that is the probability of drawing one.

Example Question #21 : How To Find The Probability Of An Outcome

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

Possible Answers:

Correct answer:

Explanation:

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

So, when looking at the event of drawing a 2 from a deck of cards, we get

It is 4 because we can draw a 2 from a deck of cards 4 different ways:

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


Now, 

because there are 52 cards in the entire deck.  Now,

We can simplify, we get

 

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

Example Question #22 : Probability

Find the probability of drawing a 9 of hearts from a deck of cards.

Possible Answers:

Correct answer:

Explanation:

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

So, when looking at the event of drawing a 9 of hearts from a deck of cards, we get

It is 1 because we can draw a 9 of hearts from a deck of cards in only 1 way:

  • 9 of hearts


Now, 

because there are 52 cards in the entire deck.  Now,

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

Example Question #22 : How To Find The Probability Of An Outcome

At Lisa's school,  of her class consists of girls. There are  students in her class. On the first day of school,  girls wore skirts. How many girls did not wear skirts?

Possible Answers:

Correct answer:

Explanation:

Given that  of the class is girls, and there are  students, we must first determine how many girls are in the class. 

Because  is double the value of ,  is double the value of should be half of .

If  of the  girls wear skirts, then we can subtract to find the number of girls not wearing skirts.

Example Question #93 : Statistics & Probability

Billy's mom baked a pizza with eight slices. Half the slices have pepperoni only. Two of the slices have both pepperoni and onions. One slice has onions only. One slice has only cheese. 

 

If Billy is allergic to pepperoni, and takes a slice of pizza with his eyes blindfolded, what is the percentage chance that he will select a piece he is not allergic to?

Possible Answers:

 

Correct answer:

 

Explanation:

The pizza that Billy's mom baked was composed of these types of slices:

Half the slices have pepperoni only. Two of the slices have both pepperoni and onoins. One slice has onions only. One slice has only cheese. 

Therefore, 

 slices had pepperoni because 

 slices had pepperoni and onions 

 slice had onion only

 slice had only cheese. 

Billy could eat either the onion only slice, or the cheese only slice. This means that out of  pieces of pizza, he could eat

Given that  is the percent equivalent of , that is the correct answer. 

Example Question #93 : Statistics & Probability

Two fair dice are thrown. What is the probability that the difference of the numbers that show on the dice will be exactly ?

Possible Answers:

Correct answer:

Explanation:

The following rolls result in the difference of the dice being :

 and the reverse of each of these.

These are  rolls out of a possible , so the probability of this event is 

 

Example Question #94 : Statistics & Probability

Two fair six-sided dice are thrown. What is the probability that the product of the two numbers rolled is between  and  inclusive?

Possible Answers:

Correct answer:

Explanation:

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 .

 

Example Question #24 : Probability

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:

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.

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