Probability and Conditional Probability Flashcards

A jar contains 4 red, 3 blue, and 5 green marbles. One marble is drawn at random. What is the probability of drawing a red or blue marble?

Answer: 7/12

Red + blue = 4 + 3 = 7 out of 12 total; P = 7/12.

The two-way table shows 240 students by grade and lunch preference. Hot Lunch Packed Lunch Grade 7 60 40 Grade 8 70 70 A Grade 8 student is selected at random. What is the probability the student prefers hot lunch?

Answer: 1/2

Grade 8 total = 70 + 70 = 140; hot lunch = 70; P = 70/140 = 1/2.

A fair coin and a fair die are both tossed. What is the probability of getting heads and an even number?

Answer: 1/4

P(heads) = 1/2; P(even on die) = 3/6 = 1/2; independent, so P = (1/2)(1/2) = 1/4.

A test has 50 questions: 20 multiple choice, 20 short answer, and 10 essay. If one question is picked at random, what is the probability it is NOT an essay question?

Answer: 4/5

Non-essay = 20 + 20 = 40; P = 40/50 = 4/5.

Events M and N are mutually exclusive with P(M) = 0.25 and P(N) = 0.40. What is P(M or N)?

Answer: 0.65

For mutually exclusive events, P(M or N) = P(M) + P(N) = 0.25 + 0.40 = 0.65.

Of 80 cars in a lot, 30 are red and 20 have sunroofs. If 10 cars are both red and have sunroofs, what is the probability a randomly chosen car is red OR has a sunroof?

Answer: 1/2

Red or sunroof = 30 + 20 − 10 = 40; P = 40/80 = 1/2.

A survey table shows 300 adults categorized by income level and vacation frequency. Vacation yearly No vacation High income 90 30 Middle income 60 60 Low income 30 30 Given that an adult takes a yearly vacation, what is the probability they have a high income?

Answer: 1/2

Total yearly vacation = 90 + 60 + 30 = 180; high income = 90; P = 90/180 = 1/2.