Theoretical probability is the expected probability of an event calculated by mathematical reasoning about equally likely outcomes, without conducting experiments. It equals the number of favorable outcomes divided by the total number of possible outcomes.
For a fair coin, you KNOW heads is 21 without flipping. You calculate based on logic: 1 favorable outcome (heads) out of 2 possible outcomes. That's theoretical - it's what SHOULD happen.
Showing a random 20 of 50 problems.
Example 1
medium
A card is drawn from a 52-card deck. What is the theoretical probability of drawing a face card (J, Q, K)?
Example 2
easy
A spinner has 4 equal sections labeled A, B, C, D. What is the theoretical probability of landing on a vowel?
Example 3
easy
A standard die is rolled. What is the theoretical probability of rolling a number less than 5?
Example 4
hard
Three fair coins are flipped. What is the theoretical probability of getting exactly two heads?Three fair coins: 8 equally likely outcomes; count the three leaves with exactly two heads
Example 5
challenge
Three fair coins are flipped. What is the theoretical probability of getting exactly two heads?Three fair coins: 8 equally likely outcomes; find those with exactly two heads
Example 6
easy
What is the theoretical probability of rolling a 7 on a single standard die?
Example 7
medium
Two standard dice are rolled. What is the theoretical probability that the sum is 10?
Example 8
medium
A bag has 4 red and 6 blue balls. One ball is drawn, replaced, and a second is drawn. What is the probability both are red?
Example 9
medium
A die is rolled. What is the theoretical probability of rolling a number that is both even and greater than 3?
Example 10
easy
A drawer has 6 black socks and 4 white socks. What is the theoretical probability of drawing a black sock at random?
Example 11
medium
A box has 5 red, 3 green, and 2 blue balls. What is the theoretical probability of drawing a ball that is not green?
Example 12
medium
A spinner has 12 equal sections numbered 1 to 12. What is the theoretical probability of landing on a factor of 12?
Example 13
easy
A card is drawn from a 52-card deck. What is the theoretical probability of drawing an ace?
Example 14
hard
A card is drawn from a 52-card deck. What is the theoretical probability that it is a red face card?
Example 15
medium
A spinner has sections of probability 21 (win) and 21 (lose). Theoretically, in 50 spins how many wins are expected?
Example 16
challenge
Three cards are dealt from a 52-card deck without replacement. What is the theoretical probability all three are hearts?
Example 17
challenge
A bag has tickets numbered 1 to 30. What is the theoretical probability of drawing a number divisible by 3 or by 5?Numbers 1–30: multiples of 3, multiples of 5, and their overlap (multiples of 15)
Example 18
hard
A box has 5 red, 4 green, and 3 blue balls. Two balls are drawn without replacement. What is the theoretical probability that both are red?
Example 19
easy
What is the theoretical probability of flipping tails on a fair coin?
Example 20
medium
A bag holds 6 white, 4 black, and 2 red marbles. What is the theoretical probability of drawing a marble that is not white?