https://file.aiquickdraw.com/mathbot/file/1737685684652x3482p8q.jpg

To solve this problem, let’s break it down into two parts, as indicated in the questions:

### Part (a): Probability that the outcome is even
From the table, we can observe that the outcomes are the products of numbers from the first and second spinner. We need to find how many of these products are even.

- **Even numbers**: Any product is even if at least one of the numbers in the multiplication is even.
- **Odd numbers**: A product is odd only if both numbers are odd.

#### First, identify the even and odd products from the table:
- **Even products**: These are products where at least one factor is an even number. 
  - From the table, the even numbers in the outcomes are: 2, 4, 6, 8, 10, 12, 6, 18, and so on.

#### Second, count the total number of outcomes:
- There are 6 possible results for each spinner (1 to 6 for the first spinner and 1 to 3 for the second spinner).
  - Total outcomes = \(6 \times 3 = 18\).

#### Count the number of outcomes with even products:
- **Even outcomes**: Products that are even in the table. These can be counted manually or identified in the table.

#### Calculate the probability:
The probability that the outcome is even = (Number of even outcomes) / (Total number of outcomes).

### Part (b): Probability when the outcome is even and greater than 11
From part (a), we already know the even outcomes. Now, we need to focus on the ones greater than 11.

#### Identify the outcomes greater than 11 that are even:
From the table, find the even numbers greater than 11.

#### Count these outcomes:
Let’s find how many of the even outcomes are greater than 11.

#### Calculate the probability:
The probability that the outcome is even and greater than 11 = (Number of even outcomes greater than 11) / (Total number of even outcomes).

---

Let me calculate these probabilities for you. Table of outcomes based on the spinner combinations
outcomes = [
    [2, 4, 6, 8, 10, 12],
    [3, 6, 9, 12, 15, 18],
    [4, 8, 12, 16, 20, 24]
]

# Flatten the table for easy processing
flattened_outcomes = [outcome for row in outcomes for outcome in row]

# Calculate total outcomes
total_outcomes = len(flattened_outcomes)

# Find even outcomes
even_outcomes = [outcome for outcome in flattened_outcomes if outcome % 2 == 0]

# Calculate probability for part (a) - probability of even outcome
probability_even = len(even_outcomes) / total_outcomes

# Find even outcomes greater than 11
even_greater_than_11 = [outcome for outcome in even_outcomes if outcome > 11]

# Calculate probability for part (b) - probability of even outcome greater than 11
probability_even_and_greater_than_11 = len(even_greater_than_11) / len(even_outcomes)

probability_even, probability_even_and_greater_than_11Here are the results for the two parts:

### Part (a): 
The probability that the outcome is even is approximately **0.83** (or 83.33%).

### Part (b):
When the outcome is even, the probability that it is also greater than 11 is approximately **0.47** (or 46.67%).

Would you like any further details on these calculations? 

Here are some related questions to explore further:
1. What would the probabilities be if the second spinner had different numbers?
2. How would the probabilities change if both spinners had even numbers only?
3. What is the probability of an outcome that is a multiple of 3?
4. How would the results change if we used a different rule for even and odd outcomes?
5. Can you calculate the probability of an odd outcome using the same approach?

**Tip:** When calculating probabilities, always make sure to identify and count all possible outcomes first before narrowing down to the ones that match the criteria you're interested in!

Two unbiased spinners are used in a game. One spinner is numbered from 1 to 6 and the other is numbered from 1 to 3. The scores on each spinner are multiplied together. The table below shows the possible outcomes. 

(a) Find the probability that the outcome is even.
(b) When the outcome is even, find the probability that it is also greater than 11.

Learn how to calculate probabilities in a game using two unbiased spinners numbered 1-6 and 1-3. The task involves determining the probability of an even outcome and the probability of an even outcome greater than 11. This problem is suitable for students in Grades 5-7 and covers key probability concepts, multiplication, and number properties.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation