Practice Events (Formal) in Math

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

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Quick Recap

A formal event is a subset of the sample space — a collection of outcomes to which a probability is assigned; events can be simple (one outcome) or compound (many outcomes).

An event is a question like 'Did I roll higher than 3?' that has yes/no answer.

Showing a random 20 of 50 problems.

Example 1

medium
Two dice are rolled. Find P(sum≄10)P(\text{sum} \ge 10).

Example 2

challenge
Rolling two dice, find P(sum=8)P(\text{sum}=8) by listing the favorable outcomes in the 36-outcome sample space.

Example 3

medium
For a die, event A={2,4,6}A=\{2,4,6\}. Describe its complement AcA^c and find P(Ac)P(A^c).

Example 4

medium
Two events on a die are mutually exclusive: A={1,2}A=\{1,2\}, B={5,6}B=\{5,6\}. Find P(AâˆȘB)P(A\cup B).

Example 5

easy
A coin is flipped. List the sample space.

Example 6

medium
If P(AâˆȘB)=0.8P(A \cup B) = 0.8, P(A)=0.5P(A) = 0.5, P(B)=0.5P(B) = 0.5, find P(A∩B)P(A \cap B).

Example 7

hard
In a group of 30 students, 18 take Spanish, 14 take French, 6 take both. Find P(Spanish or French)P(\text{Spanish or French}).

Example 8

easy
For a die, find P(rolling more than 4)P(\text{rolling more than 4}).

Example 9

medium
Three coins are flipped. Find P(exactly two heads)P(\text{exactly two heads}).

Example 10

easy
What is the probability of the sample space itself?

Example 11

easy
Is the empty set ∅\emptyset a valid event, and what is its probability?

Example 12

medium
A bag has 5 red and 3 blue marbles. Find P(red)P(\text{red}).

Example 13

easy
Drawing a card, the event 'a heart' has how many outcomes in a 52-card deck?

Example 14

medium
Two events have P(A)=0.4P(A) = 0.4, P(B)=0.5P(B) = 0.5, and they are mutually exclusive. Find P(AâˆȘB)P(A \cup B).

Example 15

easy
A die is rolled. Find P(roll a number less than 3)P(\text{roll a number less than 3}).

Example 16

medium
From a deck, draw one card. Find P(not a face card)P(\text{not a face card}).

Example 17

easy
Rolling a die, the event 'even number' is which subset of the sample space?

Example 18

easy
For a die, is the event 'roll a 4' a simple or compound event?

Example 19

medium
Rolling a die, A={odd}A = \{\text{odd}\} and B={prime}B = \{\text{prime}\}. List A∩BA \cap B and find P(A∩B)P(A \cap B).

Example 20

medium
A spinner has sectors {1,2,3,4,5,6,7,8}\{1,2,3,4,5,6,7,8\} equally likely. Find P(even)P(\text{even}).
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