Data analysis and probability — ISEE Upper practice questions

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Practice 322 Data analysis and probability questions in the app

What this topic is

Data analysis and probability on the ISEE Upper Mathematics Achievement section covers counting, set diagrams, chance, and expected value.

Students must find the probability that at least one of two conditions holds on two rolls of a number cube, sort three-club overlap to count those in exactly one group, and compute an expected number of points from a discrete reward. Questions are multi-step multiple choice. Common traps include double-counting outcomes that meet both conditions, treating pairwise overlap as if nobody belongs to all three clubs, and forgetting that remaining participants take the leftover outcome.

Answer choices usually look like nearby whole numbers or simple fractions produced by counting mistakes.

Sample questions

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

Question 1Mid

A fair six-sided number cube is rolled twice. What is the probability that the sum of the two rolls is 9 or the product of the two rolls is 20?

\dfrac{1}{18}

✗ Not this one

\dfrac{1}{12}

✗ Not this one

\dfrac{1}{9}

✓ Correct

\dfrac{1}{6}

✗ Not this one

Show answer

Answer: C — $\dfrac{1}{9}$

The pairs with sum 9 are $(3,6),(4,5),(5,4),$ and $(6,3)$ . The pairs with product 20 are $(4,5)$ and $(5,4)$ , which are already included. There are 4 favorable outcomes out of 36, so the probability is $\dfrac{4}{36}=\dfrac{1}{9}$ .

Question 2Harder

A reward system gives exactly one of three point awards. The probability of receiving 2 points is $20\%$ , and the probability of receiving 10 points is $25\%$ . All remaining participants receive 6 points. What is the expected number of points received?

2.90✗ Not this one6.00✗ Not this one6.20✓ Correct8.90✗ Not this one

Show answer

Answer: C — 6.20

The probability of receiving 6 points is $100\%-20\%-25\%=55\%$ . Thus, the expected value is $2(0.20)+6(0.55)+10(0.25)=6.20$ .

Question 3Harder

At a school, 27 students belong to the robotics club, 23 belong to the debate club, and 19 belong to the art club. The pairwise overlaps are 10, 8, and 7, and each includes the 3 students who belong to all three clubs. How many students belong to exactly one of the three clubs?

16✗ Not this one19✗ Not this one28✓ Correct47✗ Not this one

Show answer

Answer: C — 28

The pair-only regions contain $(10-3)+(8-3)+(7-3)=16$ students. Since there are 69 club memberships total, the number in exactly one club is $69-2(16)-3(3)=28$ .

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

Practice 322 Data analysis and probability questions in the app

Data analysis and probability — ISEE Upper practice questions

What this topic is

Sample questions

More ISEE Upper topics

Mathematics Achievement