Study on the flyISEE UpperQuantitative ReasoningProbability
Quantitative Reasoning
Probability is the number of favorable outcomes divided by the number of equally likely outcomes.
Questions in this topic often require counting first, using arrangements or a table of outcomes. With two dice, for example, a sum of four can happen three ways: one and three, two and two, or three and one. Arrangement problems may ask how many orders keep two items apart; counting the orders where they sit together and subtracting from the total is usually simpler.
Word problems sometimes describe group sizes through relationships, so an equation for the groups comes before the probability itself. Answers are typically fractions in lowest terms.
Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.
Question 1Harder
Five different books are to be arranged in a row on a shelf. Two of the books are a poetry book and a history book. How many arrangements have at least one book between the poetry book and the history book?
Answer: C — 72
There are total arrangements. If the poetry and history books are together, treat them as one block with 2 internal orders, giving arrangements. Therefore, arrangements keep them apart.
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?
Answer: A — Ava has a greater probability of scoring a point.
P(sum 7)=; P(sum 2 or 12)=. 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?
Answer: B —
If there are theory sheets, then , so and there are 24 blank sheets. Thus, the probability is .
Every question is picked for where you are right now, wrong answers come back until they stick, and it all works offline.
Harder than the exam: ISEE Upper Challenge · Competition-style problems
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