Probability questions
Single events, compound events, and drawing without replacement, with exact fraction answers.
Covers probability of single events like dice and coins, compound events like dice sums and card draws, and drawing without replacement from a bag of marbles.
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Sample Probability questions
1. A card is drawn at random from a standard 52-card deck. What is the probability it is a heart?+
Answer: 1/4
Step 1: A standard deck has 4 suits of 13 cards each, so there are 13 hearts out of 52 cards. Step 2: Probability = 13/52 = 1/4.
2. Two fair six-sided dice are rolled. What is the probability that the sum is 7?+
Answer: 1/6
Step 1: There are 6 × 6 = 36 equally likely outcomes for two dice. Step 2: 6 of those outcomes add up to 7. Step 3: Probability = 6/36 = 1/6.
3. Two fair six-sided dice are rolled. What is the probability that the sum is 3?+
Answer: 1/18
Step 1: There are 6 × 6 = 36 equally likely outcomes for two dice. Step 2: 2 of those outcomes add up to 3. Step 3: Probability = 2/36 = 1/18.
4. Two fair six-sided dice are rolled. What is the probability that the sum is 4?+
Answer: 1/12
Step 1: There are 6 × 6 = 36 equally likely outcomes for two dice. Step 2: 3 of those outcomes add up to 4. Step 3: Probability = 3/36 = 1/12.
5. Two fair six-sided dice are rolled. What is the probability that the sum is 6?+
Answer: 5/36
Step 1: There are 6 × 6 = 36 equally likely outcomes for two dice. Step 2: 5 of those outcomes add up to 6. Step 3: Probability = 5/36 = 5/36.
6. Two fair six-sided dice are rolled. What is the probability that the sum is 8?+
Answer: 5/36
Step 1: There are 6 × 6 = 36 equally likely outcomes for two dice. Step 2: 5 of those outcomes add up to 8. Step 3: Probability = 5/36 = 5/36.