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Probability and Conditional Probability Flashcards

7 cards from real Bluebook SAT Test practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

Read the first 7 Probability and Conditional Probability flashcards as text

  1. A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If one marble is drawn at random, what is the probability that it is NOT green?

    Answer: 4/5

    There are 8 non-green marbles out of 10 total, so P(not green) = 8/10 = 4/5.

  2. A survey of 200 students found that 120 play sports and 80 play an instrument. If 40 students do both, how many students do neither?

    Answer: 40

    Using inclusion-exclusion: sports or instrument = 120 + 80 − 40 = 160, so neither = 200 − 160 = 40.

  3. The two-way table shows pet ownership among 150 households. Cat No Cat Dog 30 45 No Dog 25 50 Given that a household has a dog, what is the probability it also has a cat?

    Answer: 2/5

    There are 30 + 45 = 75 dog households; 30 have both, so P(cat | dog) = 30/75 = 2/5.

  4. A standard die is rolled twice. What is the probability of getting a 4 on the first roll and a number greater than 2 on the second roll?

    Answer: 1/9

    P(4) = 1/6 and P(>2) = 4/6 = 2/3; since independent, multiply: (1/6)(2/3) = 2/18 = 1/9.

  5. In a class of 30 students, 18 passed the math test and 12 passed the science test. If 6 students passed both, what is the probability that a randomly selected student passed at least one test?

    Answer: 4/5

    Students passing at least one = 18 + 12 − 6 = 24; P = 24/30 = 4/5.

  6. A jar has 4 red and 6 blue chips. Two chips are drawn without replacement. What is the probability that both chips are red?

    Answer: 2/15

    P(1st red) = 4/10; P(2nd red | 1st red) = 3/9; product = 12/90 = 2/15.

  7. The table below shows 300 survey responses by age group and preference. Prefer A Prefer B Under 30 90 60 30 and over 80 70 What is the probability that a randomly chosen respondent under 30 prefers A?

    Answer: 3/5

    There are 90 + 60 = 150 respondents under 30; 90 prefer A, so P = 90/150 = 3/5.