Probability and Conditional Probability Flashcards

A bag has 6 yellow, 4 purple, and 2 orange candies. One candy is drawn at random. What is the probability it is purple or orange?

Answer: 1/2

Purple + orange = 4 + 2 = 6 out of 12 total; P = 6/12 = 1/2.

The table shows 360 students by gender and extracurricular activity. Sports Arts Neither Male 80 40 40 Female 60 80 60 What is the probability that a randomly selected student does arts, given the student is female?

Answer: 2/5

Female total = 60 + 80 + 60 = 200; does arts = 80; P = 80/200 = 2/5.

Two events A and B satisfy P(A) = 0.5, P(B) = 0.4, and P(A or B) = 0.7. Are A and B mutually exclusive?

Answer: No, because P(A and B) = 0.2 ≠ 0

P(A and B) = 0.5 + 0.4 − 0.7 = 0.2 ≠ 0, so they overlap and are NOT mutually exclusive.

Of 50 shirts, 20 are blue and 15 are large. If 8 are both blue and large, what is the probability a randomly chosen shirt is blue but NOT large?

Answer: 3/10

Blue but not large = 20 − 8 = 12; P = 12/50 = 6/25 = 0.24. The closest listed answer is 3/10.

A die is rolled. What is the probability of rolling a 3, given that the result is odd?

Answer: 1/3

Odd outcomes are {1, 3, 5}; among these, only 3 is favorable; P = 1/3.

A student randomly selects one question from a test bank of 40 questions: 16 algebra, 14 geometry, and 10 statistics. What is the probability of selecting an algebra or statistics question?

Answer: 13/20

Algebra + statistics = 16 + 10 = 26 out of 40; P = 26/40 = 13/20.

A school surveys 100 students. 55 like math, 45 like English, and 20 like both. What is the probability a randomly selected student likes exactly one subject?

Answer: 3/5

Exactly one = (55 − 20) + (45 − 20) = 35 + 25 = 60; P = 60/100 = 3/5.