ISEE Lower Level

Probability

Simple and compound probability, independent and dependent events, expected values

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Have you ever tried to guess what’s for dinner before you smell it? If it’s Friday, there’s a really good chance it’s pizza! 🍕 That "chance" is what mathematicians call probability. Probability is just a fancy way of asking, "How likely is something to happen?"

It’s a huge part of the ISEE, showing up in both the Quantitative Reasoning and Mathematics Achievement sections. We measure probability on a scale from (no way, like a T-Rex showing up to take your test 🦖) to (definitely happening, like you doing an awesome job!). Most of the time, probability lives right in the middle as a fraction.

Think of a giant gumball machine. If there are gumballs and are your favorite blue raspberry flavor, your chance of getting a blue one is out of . On the ISEE, we write that as the fraction . The bottom number (denominator) is always the total number of things, and the top number (numerator) is the number of winning things!

Sometimes, the ISEE will ask you to figure out the chances of two things happening in a row. Like getting a blue gumball AND rolling a on a dice. Here is a secret test trick: when you want one thing AND another thing to happen, you multiply their probabilities together! 🎲 Get ready to be a probability pro!

Key Formula
To find the chance of something happening, use this rule:

Practice Questions

4 practice questions for ISEE Lower Level

Q1 Easy
A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If one marble is drawn at random, what is the probability of drawing a blue marble?
A
B
C
D
Show Solution
  • Probability is found by dividing the number of favorable outcomes by the total number of outcomes. There are 3 blue marbles (favorable outcomes) and a total of marbles. The probability of drawing a blue marble is .
Answer: B
Q2 Easy
A spinner is divided into 8 equal sections numbered 1 through 8. What is the probability of spinning an even number?
A
B
C
D
Show Solution
  • The even numbers from 1 to 8 are 2, 4, 6, and 8. That gives 4 favorable outcomes out of 8 total sections. .
Answer: D
Q3 Easy
A jar holds 12 candies: 4 cherry, 5 lemon, and 3 orange. If one candy is chosen at random, what is the probability of choosing a cherry or orange candy?
A
B
C
D
Show Solution
  • Cherry candies (4) and orange candies (3) together make favorable outcomes. The total number of candies is 12. The probability is .
Answer: C
Q4 Easy
A deck of 20 cards is numbered 1 through 20. One card is chosen at random. What is the probability that the card shows a multiple of 4?
A
B
C
D
Show Solution
  • The multiples of 4 from 1 to 20 are: 4, 8, 12, 16, and 20. That is 5 favorable outcomes out of 20 total. .
Answer: C

Tips & Strategies

  • The 'AND' vs 'OR' rule! On the ISEE, if you need Event A AND Event B to happen, multiply their fractions. If you need Event A OR Event B (and they can't both happen at the same time), add their fractions!
  • The 'NOT' trick! If a question asks for the probability of something NOT happening, find the probability of it happening, and subtract it from (like ).
  • Always simplify your fractions! The ISEE loves to hide the correct answer by reducing it. If you get , look for in the answer choices.

Common Mistakes

  • Watch out for 'without replacement'! 🛑 If a problem says someone takes a marble and keeps it, the total number of marbles for the next draw goes down by .
  • Don't forget to count all the possibilities in coin flips. Flipping Heads then Tails is a different outcome than flipping Tails then Heads!

Frequently Asked Questions

Do I need to simplify my fractions on the ISEE?

Yes! The ISEE almost always simplifies fractions in the answer choices. If you calculate , you should expect to see as the correct choice.

What does 'independent event' mean?

It means the first event doesn't change the chances of the second event! Like flipping a coin twice: the coin doesn't remember what it landed on the first time.

What is Quantitative Comparison?

It's a special question format on the ISEE Quantitative Reasoning section where you compare Column A and Column B. You just need to figure out which side is bigger, or if they are perfectly equal!

Is there a penalty for guessing on the ISEE?

Nope! You never lose points for a wrong answer on the ISEE. If you are stuck on a tough probability question, take your best guess and move on to the next one! ✨

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