Probability — ISEE Upper practice questions

37 questions on the paper
89 practice questions in the app
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Practice 89 Probability questions in the app

What this topic is

On the ISEE Upper Quantitative Reasoning section, Probability covers chance, counting, and equally likely outcomes in multi-step word problems.

A student has to model pairings, compare dice-sum likelihoods, and find the chance of drawing one type of item after using algebra to recover hidden counts. Questions often ask which statement is true about two events or ask for a probability after a short setup.

Answer choices are typically fractions, comparative statements, or a whole number. Common traps include treating every dice sum as equally likely, mixing pair counts with permutations, and dividing before the parts of the collection are known.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

Question 1Harder

In a club, each pair of members shakes hands exactly once. If 10 new members joined the club and then each pair of members shook hands exactly once, the total number of handshakes would increase by 155. How many members were originally in the club?

9✗ Not this one10✗ Not this one11✓ Correct15✗ Not this one

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Answer: C — 11

If there were originally $n$ members, the 10 new members create $10n$ handshakes with original members and $\dfrac{10\times9}{2}=45$ handshakes among themselves. Thus $10n+45=155$ , so $n=11$ .

Question 2Easier

Ava and Ben each roll two fair dice numbered 1 through 6 and record the sum. Ava scores a point if her sum is 7. Ben scores a point if his sum is 2 or 12. Which statement is true?

Ava has a greater probability of scoring a point.✓ CorrectBen has a greater probability of scoring a point.✗ Not this oneAva and Ben have the same probability of scoring a point.✗ Not this oneThere is not enough information to determine who has the greater probability.✗ Not this one

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Answer: A — Ava has a greater probability of scoring a point.

P(sum 7)= $6/36$ ; P(sum 2 or 12)= $2/36$ . Ava is more likely.

Question 3Mid

A music folder contains 45 sheets. The number of practice sheets is 5 more than the number of theory sheets, and the number of blank sheets is 3 times the number of theory sheets. One sheet is chosen at random. What is the probability that the chosen sheet is blank?

\dfrac{8}{45}

✗ Not this one

\dfrac{8}{15}

✓ Correct

\dfrac{13}{45}

✗ Not this one

\dfrac{7}{15}

✗ Not this one

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Answer: B — $\dfrac{8}{15}$

If there are $t$ theory sheets, then $t+(t+5)+3t=45$ , so $t=8$ and there are 24 blank sheets. Thus, the probability is $\dfrac{24}{45}=\dfrac{8}{15}$ .

Every question is picked for where you are right now, wrong answers come back until they stick, and it all works offline.

Practice 89 Probability questions in the app

Probability — ISEE Upper practice questions

What this topic is

Sample questions

More ISEE Upper topics

Quantitative Reasoning