Math Problem Statement
Solution
Let's first go through the details provided in the question and use that information to complete the frequency tree and calculate the probability:
Given information:
- Total number of children: 80
- Number of girls: 36
- Number of boys: 80 - 36 = 44
- Number of children who failed the test: 9
- Number of boys who passed the test: 39
- This means 44 boys - 39 boys who passed = 5 boys who failed the test.
For the frequency tree:
- The total number of children is 80.
- 36 of these children are girls, so 80 - 36 = 44 boys.
- Out of the 80 children, 9 failed the test, so 80 - 9 = 71 passed.
- We know that 39 boys passed the test. Therefore, the number of boys who failed the test is 44 - 39 = 5.
- For the girls, since 9 failed the test in total and 5 boys failed, this means the remaining 4 children who failed must be girls.
Now, let's fill out the frequency tree based on this information.
For part (b):
You are asked to find the probability that a boy who is chosen at random failed the test.
- Total number of boys = 44
- Number of boys who failed = 5
The probability is calculated as:
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Math Problem Analysis
Mathematical Concepts
Probability
Frequency Trees
Formulas
Probability = (Number of favorable outcomes) / (Total outcomes)
Theorems
Basic probability theory
Suitable Grade Level
Grades 7-9
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