Compound events are probability events made up of two or more simple events combined using 'and' (both events occur) or 'or' (at least one occurs). For independent 'and' events, multiply probabilities; for 'or' events, add probabilities and subtract any overlap.
Simple event: rolling a 6. Compound event: rolling a 6 AND then flipping heads. For 'and,' multiply probabilities. For 'or,' add them (but subtract overlap if any).
Showing a random 20 of 50 problems.
Example 1
hard
Two dice are rolled. What is P(at least one die shows a 5)?
Example 2
easy
A spinner lands red with P=31 each spin. What is P(red three spins in a row)?
Example 3
easy
Two dice are rolled. What is P(both show a 1)?
Example 4
easy
Three coins are flipped. What is P(all tails)?Three coins flipped — find P(all tails)
Example 5
medium
P(A)=0.6, P(B)=0.4, and A and B are independent. Find P(A and B) and P(A or B).P(A)=0.6, P(B)=0.4, independent — find P(A and B) and P(A or B)
Example 6
medium
Two cards are drawn from a deck without replacement. What is P(both hearts)?
Example 7
challenge
A bag has 5 red and 5 blue. Two drawn without replacement. What is P(both same color)?
Example 8
challenge
Three dice are rolled. What is P(at least one shows a 6)?
Example 9
hard
A bag has 3 red, 4 blue, 5 green marbles. Two are drawn without replacement. What is P(one red and one blue), in either order?
Example 10
easy
A card is drawn from a deck. What is P(a king or a queen)?
Example 11
medium
Two dice are rolled. What is P(sum of 7 or sum of 11)?
Example 12
easy
A coin is flipped and a die is rolled. What is P(heads and a 4)?Coin flip then die roll — find P(H and 4)
Example 13
hard
Three cards are drawn from a 52-card deck without replacement. What is P(all three are aces)?
Example 14
easy
Two coins are flipped. What is P(both heads)?Two coin flips — find P(both heads)
Example 15
easy
A bag has 5 red and 5 blue marbles. Two marbles are drawn with replacement. What is P(red then blue)?Two marbles drawn with replacement — find P(red then blue)
Example 16
hard
A coin is flipped 5 times. What is P(exactly 3 heads)?
Example 17
easy
A die is rolled. What is P(even or a 3)?
Example 18
medium
A card is drawn. What is P(a spade or a face card)?Spades and Face Cards in a 52-card deck — find P(spade or face card)
Example 19
easy
A card is drawn from a 52-card deck. What is P(a heart or a spade)?
Example 20
easy
A spinner lands red with P=41 each spin. Spun twice, what is P(red both times)?Spinner spun twice — find P(red both times)