Instructions
Read each scenario below. For each question, decide which of the two outcomes is more likely to happen. Circle or write down the more likely outcome and briefly explain your reasoning. If both outcomes are equally likely, state that. Good luck!
Part 1: Classic Chances
1. Rolling a Standard Die:
You roll a standard six-sided die once. Which is more likely?
- A) Rolling an even number (2, 4, or 6)
- B) Rolling a number greater than 4 (5 or 6)
More Likely Outcome & Reasoning:
2. Flipping a Coin:
You flip a fair coin two times. Which is more likely?
- A) Getting two heads (HH)
- B) Getting one head and one tail (in any order, HT or TH)
More Likely Outcome & Reasoning:
3. Another Roll of the Die:
You roll a standard six-sided die once again. Which is more likely?
- A) Rolling a number less than 3 (1 or 2)
- B) Rolling a prime number less than 5 (2 or 3)
More Likely Outcome & Reasoning:
Part 2: The Marble Bag Challenge
4. Bag of Marbles:
A bag contains 7 red marbles, 4 blue marbles, and 6 green marbles. If you reach in and pull one marble out without looking, which color are you more likely to draw?
- A) A blue marble
- B) A red marble
More Likely Outcome & Reasoning:
5. Comparing Two Bags:
You have two bags of marbles:
- Bag X contains 3 black marbles and 2 white marbles (5 total).
- Bag Y contains 7 black marbles and 4 white marbles (11 total).
From which bag are you more likely to draw a black marble?
More Likely Bag & Reasoning:
Part 3: Spinner Decisions
6. The School Fair Spinner:
A spinner for a game is divided into 10 equal sections. 5 sections are Red, 2 sections are Yellow, and 3 sections are Blue.
Which is more likely after one spin?
- A) Landing on Blue
- B) Landing on Red
More Likely Outcome & Reasoning:
7. Two Different Spinners:
You get to choose one of two spinners to try and win a prize by landing on the "Win" section.
- Spinner A is divided into 3 equal parts: Win, Lose, Try Again.
- Spinner B is divided into 5 equal parts: Win, Lose, Lose, Try Again, Try Again.
Which spinner gives you a better chance of landing on "Win"?
More Likely Spinner & Reasoning:
Part 4: Real-World Probability
8. Weekend Weather:
The weather forecast for the weekend is in. On Saturday, there is a 60% chance of sunshine. On Sunday, there is a 2/3 chance of sunshine. Which day is more likely to be sunny?
More Likely Day & Reasoning:
9. Drawing a Card:
You are playing a game with a standard 52-card deck. The deck is evenly split into four suits: 13 Hearts, 13 Diamonds, 13 Spades, and 13 Clubs. To win, you must draw a Spade. So far, 10 cards have been drawn, and 4 of them were Spades. On the next draw from the remaining cards, which is more likely?
- A) Drawing a Spade
- B) Drawing a card that is NOT a Spade
More Likely Outcome & Reasoning:
Answer Key
1. More Likely Outcome: A) Rolling an even number.
Reasoning: There is a 3/6 (or 1/2) chance of rolling an even number, but only a 2/6 (or 1/3) chance of rolling a number greater than 4. 3/6 is greater than 2/6.
2. More Likely Outcome: B) Getting one head and one tail.
Reasoning: There are four possible outcomes: HH, HT, TH, TT. Only one outcome is HH (a 1/4 chance). Two outcomes result in one head and one tail (HT and TH), making the chance 2/4 (or 1/2). 2/4 is greater than 1/4.
3. More Likely Outcome: They are equally likely.
Reasoning: The chance of rolling a number less than 3 (1 or 2) is 2/6. The chance of rolling a prime number less than 5 (2 or 3) is also 2/6. The probabilities are the same.
4. More Likely Outcome: B) A red marble.
Reasoning: There are 7 red marbles and only 4 blue marbles. Since there are more red marbles, the probability of drawing one is higher (7/17 vs 4/17).
5. More Likely Bag: Bag X.
Reasoning: In Bag X, the probability of drawing a black marble is 3/5. In Bag Y, the probability is 7/11. To compare, we can find a common denominator (55) or convert to decimals. 3/5 = 0.60. 7/11 is approximately 0.636. Wait, let me recheck that. 3/5 = 33/55. 7/11 = 35/55. So Bag Y is more likely. Let's correct that.
Correction: More Likely Bag: Bag Y.
Reasoning: In Bag X, the probability of drawing a black marble is 3/5 (or 60%). In Bag Y, the probability is 7/11 (approximately 63.6%). Since 7/11 is a slightly larger fraction than 3/5, you are more likely to draw a black marble from Bag Y.
6. More Likely Outcome: B) Landing on Red.
Reasoning: The chance of landing on Red is 5/10 (or 1/2). The chance of landing on Blue is 3/10. 5/10 is greater than 3/10.
7. More Likely Spinner: Spinner A.
Reasoning: Spinner A has a 1/3 chance of winning. Spinner B has a 1/5 chance of winning. 1/3 is a larger probability than 1/5.
8. More Likely Day: Sunday.
Reasoning: Saturday's chance of sun is 60%. Sunday's chance is 2/3. To compare, convert 2/3 to a percentage: (2 ÷ 3) * 100 ≈ 66.7%. Since 66.7% is greater than 60%, Sunday is more likely to be sunny.
9. More Likely Outcome: B) Drawing a card that is NOT a Spade.
Reasoning: There are 52 - 10 = 42 cards left in the deck. There were 13 Spades, and 4 were drawn, so there are 13 - 4 = 9 Spades left. The number of non-Spade cards left is 42 - 9 = 33. The chance of drawing a Spade is 9/42, while the chance of drawing a non-Spade is 33/42. It is much more likely to draw a card that is not a Spade.