Math Problem Statement

80 children sat a test. 36 of the children are girls. 9 of the 80 children failed the test. 39 of the boys passed the test. (a) Use this information to complete the frequency tree. (b) Work out the probability that the boy failed the test.

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:

  1. The total number of children is 80.
  2. 36 of these children are girls, so 80 - 36 = 44 boys.
  3. Out of the 80 children, 9 failed the test, so 80 - 9 = 71 passed.
  4. We know that 39 boys passed the test. Therefore, the number of boys who failed the test is 44 - 39 = 5.
  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:

Probability=Number of boys who failedTotal number of boys=544\text{Probability} = \frac{\text{Number of boys who failed}}{\text{Total number of boys}} = \frac{5}{44}

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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