To solve the problem, we need to calculate the probability of each event. The general formula for probability is:
\[
\text{Probability} = \frac{\text{Number of ways the event can happen}}{\text{Number of possible outcomes}}
\]
Let's go through each event step by step.
---
Event #1: Rolling an even number on a 6-sided die
-
Number of ways the event can happen: The even numbers on a 6-sided die are 2, 4, and 6. So, there are 3 favorable outcomes.
-
Number of possible outcomes: A 6-sided die has 6 possible outcomes (1, 2, 3, 4, 5, 6).
\[
\text{Probability} = \frac{3}{6} = \frac{1}{2}
\]
---
Event #2: Rolling a 12-sided die and getting a 2 or a 3
-
Number of ways the event can happen: The favorable outcomes are rolling a 2 or a 3. So, there are 2 favorable outcomes.
-
Number of possible outcomes: A 12-sided die has 12 possible outcomes.
\[
\text{Probability} = \frac{2}{12} = \frac{1}{6}
\]
---
Event #3: Pulling a striped marble from the bag
From the image, the bag contains:
- 3 striped marbles
- 7 non-striped marbles
-
Number of ways the event can happen: There are 3 striped marbles.
-
Number of possible outcomes: There are a total of \(3 + 7 = 10\) marbles.
\[
\text{Probability} = \frac{3}{10}
\]
---
Event #4: Flipping two coins at the same time and getting tails on both
-
Number of ways the event can happen: When flipping two coins, the only way to get tails on both is "TT". So, there is 1 favorable outcome.
-
Number of possible outcomes: The possible outcomes when flipping two coins are: HH, HT, TH, TT. So, there are 4 possible outcomes.
\[
\text{Probability} = \frac{1}{4}
\]
---
Event #5: Rolling an odd number on a 12-sided die
-
Number of ways the event can happen: The odd numbers on a 12-sided die are 1, 3, 5, 7, 9, and 11. So, there are 6 favorable outcomes.
-
Number of possible outcomes: A 12-sided die has 12 possible outcomes.
\[
\text{Probability} = \frac{6}{12} = \frac{1}{2}
\]
---
Event #6: Pulling any marble other than white from the bag
From the image, the bag contains:
- 3 white marbles
- 7 non-white marbles
-
Number of ways the event can happen: There are 7 marbles that are not white.
-
Number of possible outcomes: There are a total of \(3 + 7 = 10\) marbles.
\[
\text{Probability} = \frac{7}{10}
\]
---
Final Answers
1. Event #1: \(\frac{1}{2}\)
2. Event #2: \(\frac{1}{6}\)
3. Event #3: \(\frac{3}{10}\)
4. Event #4: \(\frac{1}{4}\)
5. Event #5: \(\frac{1}{2}\)
6. Event #6: \(\frac{7}{10}\)
\[
\boxed{\frac{1}{2}, \frac{1}{6}, \frac{3}{10}, \frac{1}{4}, \frac{1}{2}, \frac{7}{10}}
\]
Parent Tip: Review the logic above to help your child master the concept of chance and probability worksheet.
