Practice Compound Probability in Math

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

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Quick Recap

The probability of two or more events occurring together (P(A and B)P(A \text{ and } B)) or at least one occurring (P(A or B)P(A \text{ or } B)), accounting for whether the events are independent or dependent.

Single-event probability asks about one thing happening. Compound probability asks about combinations: 'What's the chance of rolling a 6 AND flipping heads?' or 'What's the chance of drawing a heart OR a face card?' The word 'and' usually means multiply; the word 'or' usually means add (but subtract the overlap).

Showing a random 20 of 50 problems.

Example 1

medium
Two cards are drawn without replacement from a deck. Find P(both aces)P(\text{both aces}).

Example 2

medium
A coin is flipped 4 times. Find P(exactly 2 heads)P(\text{exactly 2 heads}).

Example 3

easy
Two fair coins are flipped. Find P(at least one head)P(\text{at least one head}).

Example 4

easy
A bag has 3 red and 2 blue marbles. Draw one. Find P(red or blue)P(\text{red or blue}).

Example 5

easy
A spinner has 4 equal sections numbered 1-4, spun twice. Find P(first is 1 and second is 1)P(\text{first is 1 and second is 1}).

Example 6

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

Example 7

challenge
In a class, 60%60\% play soccer, 30%30\% play tennis, and 20%20\% play both. Find P(a student plays neither)P(\text{a student plays neither}).

Example 8

medium
A bag has 6 red, 4 blue marbles. Draw 2 without replacement. Find P(both blue)P(\text{both blue}).

Example 9

easy
Two fair coins are flipped. Find P(both heads)P(\text{both heads}).

Example 10

medium
A die is rolled 3 times. Find P(at least one 6)P(\text{at least one 6}).

Example 11

hard
A drawer has 6 socks: 4 black, 2 white. Pull 2 randomly. Find P(match)P(\text{match}).

Example 12

medium
P(A)=0.5P(A)=0.5, P(B∣A)=0.6P(B|A)=0.6. Find P(A∩B)P(A\cap B).

Example 13

medium
A bag has 4 red and 6 green marbles. Two are drawn without replacement. Find P(both red)P(\text{both red}).

Example 14

easy
A coin is flipped and a die rolled. Find P(tails and an even number)P(\text{tails and an even number}).

Example 15

challenge
In a group of 23 people, find P(at least 2 share a birthday)P(\text{at least 2 share a birthday}), ignoring leap years. (Express via the standard formula.)

Example 16

hard
Three independent traffic lights have P(green)=0.4P(\text{green})=0.4 each. Find P(exactly 2 green)P(\text{exactly 2 green}).

Example 17

challenge
5 people randomly sit in a row of 5 chairs. Find P(Alex and Bo sit next to each other)P(\text{Alex and Bo sit next to each other}).

Example 18

medium
Two dice are rolled. Find P(sum=7)P(\text{sum} = 7).

Example 19

easy
P(A)=0.3P(A)=0.3, P(B)=0.5P(B)=0.5, and A and B are mutually exclusive. Find P(A∪B)P(A \cup B).

Example 20

easy
A card is drawn from a standard deck. Find P(heart or spade)P(\text{heart or spade}).
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