Practice Basic Probability in Statistics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

Probability is the measure of how likely an event is to occur, expressed as a number between 0 (impossible) and 1 (certain). It is calculated as the ratio of favorable outcomes to total possible outcomes when all outcomes are equally likely.

Probability is a way of putting a number on chance. Flipping heads? That's 0.50.5 (half the time). Rolling a 6 on a die? That's 16\frac{1}{6} (one out of six possible outcomes). It's like asking 'if we did this many times, what fraction would this outcome happen?'

Showing a random 20 of 50 problems.

Example 1

easy
A fair six-sided die is rolled. What is the probability of rolling an even number?

Example 2

medium
From 11 to 5050, find the probability that a randomly chosen number is a perfect square.

Example 3

hard
A spinner has 55 sections labeled 1,2,3,4,51, 2, 3, 4, 5. The probability of landing on each section is proportional to its label. What is the probability of landing on 33?

Example 4

hard
A bag has 44 red, 66 green, and 1010 blue marbles. Find P(not green)P(\text{not green}).

Example 5

medium
A die is rolled. What is the probability of rolling a prime number?

Example 6

medium
A standard die is rolled. What is the probability of rolling a number less than 55?

Example 7

hard
A spinner has 88 sections, 33 red and 55 blue. After 8080 spins, red came up 2424 times. Compute both the theoretical and experimental probability of red.

Example 8

medium
A card is drawn from a 52-card deck. What is the probability of drawing a red face card (J, Q, K of hearts or diamonds)?

Example 9

easy
A coin is flipped. What is the probability of tails?

Example 10

easy
P(rain)=0.4P(\text{rain}) = 0.4. What is P(no rain)P(\text{no rain})?

Example 11

easy
Probabilities are numbers in what range?

Example 12

medium
A die is rolled. What is the probability of rolling an odd number?

Example 13

medium
A bag has tickets numbered 11 to 3030. What is the probability of drawing a multiple of 77?

Example 14

easy
A bag has 3 red and 2 blue marbles. What is the probability of drawing a red marble?

Example 15

medium
From a deck of 5252 cards, what is the probability of drawing a card that is either red or a queen?

Example 16

hard
A bag has 2020 marbles: 55 red, 88 blue, 77 green. What is the probability of drawing a marble that is red OR blue?

Example 17

medium
A spinner has sections colored red (probability 0.250.25), blue (0.350.35), and green. What is the probability of green?

Example 18

easy
What is the probability of an impossible event?

Example 19

medium
A bag has marbles numbered 1 to 20. What is the probability of drawing a multiple of 5?

Example 20

easy
A fair die is rolled. What is the probability of rolling a 66?