SSAT Middle Level

Probability

Q: How do I know whether to add or multiply fractions in probability?

If you want event A **AND** event B to happen (like drawing two red marbles in a row), you multiply. If you want event A **OR** event B to happen (like drawing a red marble or a blue marble on a single try), you add.

Q: Is probability always a fraction?

Usually! It is most often written as a fraction like `\frac{1}{4}`, but it can also be written as a decimal (0.25) or a percentage (25%).

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

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Have you ever reached into a giant bowl of Halloween candy blindfolded and hoped to pull out a chocolate bar instead of a boring mint? 🍫 That feeling of hoping for a specific outcome is exactly what probability is all about! Probability is just the math way of asking, "How likely is this to happen?"

To find the probability of something, you just need to know two things: what you want to happen (like getting chocolate), and everything that could possibly happen (every single piece of candy in the bowl). You just put what you want on top of what is possible to make a fraction! 🍕 For example, if a pizza has 8 slices and 2 of them have pepperoni, your chance of grabbing a pepperoni slice in the dark is $\frac{2}{8}$ .

On the SSAT, you will see a lot of questions about bags of colorful marbles, spinning game wheels, or drawing cards. Sometimes they ask about doing something once (simple probability), and sometimes they ask about doing it twice in a row (compound probability). Don't worry, the math is exactly the same! You just have to read carefully to see if you put the marble back in the bag before drawing again. You've got this! 🎲

Key Formula

Probability = \frac{Number of winning outcomes}{Total number of possible outcomes}

Practice Questions

3 practice questions for SSAT Middle Level

Q1 Medium

A fruit basket contains 6 apples, 5 oranges, 3 pears, and 10 bananas. If Sarah selects a piece of fruit at random, what is the probability that she will select an orange or a pear?

\frac{1}{8}

\frac{1}{4}

\frac{1}{3}

\frac{5}{12}

\frac{1}{2}

Show Solution

First, find the total number of pieces of fruit in the basket: 6 + 5 + 3 + 10 = 24. Next, find the total number of oranges and pears: 5 oranges + 3 pears = 8. The probability of selecting an orange or a pear is the number of oranges and pears divided by the total number of pieces of fruit, which is $\frac{8}{24}$ . This fraction reduces to $\frac{1}{3}$ .

Answer: C

Q2 Medium

There are 30 pairs of socks in a drawer. Of these, 12 are black, 8 are white, 4 are gray, and the rest are navy. If David selects a pair of socks at random, what is the probability that he will select a navy pair?

\frac{1}{6}

\frac{1}{5}

\frac{4}{15}

\frac{1}{3}

\frac{2}{5}

Show Solution

First, find the number of navy pairs of socks. The total number of pairs is 30, and there are 12 black, 8 white, and 4 gray pairs. Subtract these from the total to find the navy pairs: 30 - (12 + 8 + 4) = 30 - 24 = 6 navy pairs. The probability of selecting a navy pair is the number of navy pairs divided by the total number of pairs: $\frac{6}{30}$ . Dividing the numerator and denominator by 6 gives $\frac{1}{5}$ .

Answer: B

Q3 Medium

A jar contains 10 pennies, 6 nickels, 5 dimes, and 4 quarters. If a coin is drawn at random from the jar, what is the probability that the coin is NOT a penny?

\frac{1}{5}

\frac{2}{5}

\frac{1}{2}

\frac{3}{5}

\frac{4}{5}

Show Solution

First, find the total number of coins in the jar: 10 + 6 + 5 + 4 = 25 coins. Since there are 10 pennies, the number of coins that are NOT pennies is 25 - 10 = 15. The probability of selecting a coin that is not a penny is $\frac{15}{25}$ . Both numbers are divisible by 5, so this fraction reduces to $\frac{3}{5}$ .

Answer: D

Tips & Strategies

Always circle the words 'with replacement' or 'without replacement' in the question. If it says 'without', remember to subtract 1 from the top AND bottom of your fraction for the second draw!
Simplify your fractions as early as possible. Multiplying $\frac{1}{2} \cdot \frac{4}{9}$ is much easier than multiplying $\frac{5}{10} \cdot \frac{4}{9}$ without a calculator.
If a question asks for the probability of 'at least one' of something happening, find the probability of it NEVER happening, and subtract that from 1. It saves so much time!

Common Mistakes

Watch out for forgetting to change the total number of items! If you eat a piece of candy from a bag, there is one less piece of candy overall. Your denominator MUST change for the next draw.
Don't forget that when you want two things to happen in a row (like drawing a red marble AND a blue marble), you must MULTIPLY the fractions, not add them.

Frequently Asked Questions

What does 'without replacement' mean?

It means once you take an item out (like a marble or a card), you keep it out! You do not put it back before drawing the next one. This changes the total number of items left.

How do I know whether to add or multiply fractions in probability?

If you want event A AND event B to happen (like drawing two red marbles in a row), you multiply. If you want event A OR event B to happen (like drawing a red marble or a blue marble on a single try), you add.

Is probability always a fraction?

Usually! It is most often written as a fraction like $\frac{1}{4}$ , but it can also be written as a decimal (0.25) or a percentage (25%).

Will I get to use a calculator for these big fractions on the SSAT?

Nope, there are no calculators allowed on the SSAT. But don't panic! The test makers design the numbers so they will simplify nicely if you look for common factors.

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