Questions: Simple Probability

Question 1

A bag contains 4 red, 3 blue, and 3 green marbles. You pick one at random. What is the probability of picking a red marble?

• A. 4/3
• B. 3/10
• C. 4/10
• D. 1/4

Answer: (C)

There are 4 + 3 + 3 = 10 total equally likely outcomes and 4 favorable ones (the red marbles), so P(red) = 4/10 = 2/5. The option 1/4 is wrong because it ignores the green marbles; 3/10 is the probability for blue, not red.

Question 2

If you flip a fair coin 5 times and get heads most of the time, the probability of getting tails on the 6th flip is greater than 1/2.

• T. True
• F. False

Answer: False

Each coin flip is an independent event — the coin has no memory of past results. The probability of tails on any fair flip is always exactly 1/2, regardless of what came before. The belief that past results influence future independent outcomes is called the gambler's fallacy.

Question 3

A fair six-sided die is rolled. What is the sample space, and what is the probability of rolling an even number?

Model answer: Sample space: {1, 2, 3, 4, 5, 6}. P(even) = 3/6 = 1/2.

Listing all possible outcomes first — the sample space — is the essential first step. There are 6 equally likely outcomes. Three of them are even (2, 4, 6), so the probability is 3/6, which simplifies to 1/2. Expressing this as a decimal (0.5) or percent (50%) are equally valid.