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Probability — SSAT Upper practice questions

Probability on the SSAT Upper Quantitative (Math) section covers equally likely outcomes, complements, combined events joined by or, and properties of random integers. A student has to identify the sample space, count favorable cases, and write the chance as a simplified fraction. Items are short multiple-choice word problems: a counter drawn from a bag, two different integers chosen from a consecutive list, or a person picked from groups that each chose one activity. Common traps include answering the complementary event, requiring both factors to be even for an even product, and multiplying instead of adding when events cannot both occur. Answer choices are typically simplified fractions that look similar.

  • Section: Quantitative (Math) 50 questions on the paper
  • 135 practice questions in the app

Sample questions

Question 1

A bag contains 5 red counters and 4 white counters. If one counter is selected at random, what is the probability that the counter will not be red?

  1. A19\dfrac{1}{9}
  2. B49\dfrac{4}{9}
  3. C59\dfrac{5}{9}
  4. D45\dfrac{4}{5}
  5. E54\dfrac{5}{4}
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Answer: B — 49\dfrac{4}{9}

There are 4 white counters and 5+4=95+4=9 counters total. The probability of not red is 49\dfrac{4}{9}.

Question 2

Two different integers are selected at random from the integers 1 through 12. What is the probability that their product is even?

  1. A522\dfrac{5}{22}
  2. B12\dfrac{1}{2}
  3. C34\dfrac{3}{4}
  4. D1722\dfrac{17}{22}
  5. E3544\dfrac{35}{44}
Show answer

Answer: D — 1722\dfrac{17}{22}

The product is odd only if both selected integers are odd. There are 6 odd integers from 1 through 12, so the probability of selecting two odd integers is 612⋅511=522\dfrac{6}{12}\cdot\dfrac{5}{11}=\dfrac{5}{22}. Therefore, the probability that the product is even is 1−522=17221-\dfrac{5}{22}=\dfrac{17}{22}.

Question 3

At a workshop, each person chose exactly one of four activities: 18 people chose Drawing, 12 chose Strategy games, 15 chose Robotics, and 9 chose Music. If one person is selected at random, what is the probability that the person chose Drawing or Robotics?

  1. A518\dfrac{5}{18}
  2. B12\dfrac{1}{2}
  3. C1118\dfrac{11}{18}
  4. D23\dfrac{2}{3}
  5. E79\dfrac{7}{9}
Show answer

Answer: C — 1118\dfrac{11}{18}

Drawing or Robotics accounts for 18+15=3318+15=33 people. The total is 18+12+15+9=5418+12+15+9=54, and 33/54=11/1833/54=11/18.

Practice 135 Probability questions in the app

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