AI Math Solver
Resources
Questions
Pricing
Login
Register
Home
>
Questions
>
Calculate the Probability of a Female Teenager with Favourite Hobby Watching Films from a Two-Way Table
Mathematics
Grade 7 (Junior High School)
Question Content
A group of teenagers are asked about their favourite hobbies. The results are shown in the following table:\n| | Sports | Playing video games | Watching films | Total |\n|----------|--------|---------------------|----------------|-------|\n| Male | 9 | 2 | 3 | 14 |\n| Female | 7 | 3 | 8 | 18 |\n| Total | 16 | 5 | 11 | 32 |\nQ6a. In fractions, what is the probability that a teenager selected at random is female and their favourite hobby is watching films? You can simplify this fraction if you wish.
Correct Answer
1/4
Detailed Solution Steps
1
Step 1: Identify the number of favorable outcomes. From the table, the number of female teenagers whose favourite hobby is watching films is 8.
2
Step 2: Identify the total number of possible outcomes. The total number of teenagers surveyed is the grand total in the table, which is 32.
3
Step 3: Calculate the probability by dividing the number of favorable outcomes by the total number of outcomes: 8/32.
4
Step 4: Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (8). 8 ÷ 8 = 1, 32 ÷ 8 = 4, so the simplified fraction is 1/4.
Knowledge Points Involved
1
Basic Probability Calculation
Basic probability is calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes, expressed as P(event) = (Number of favorable outcomes) / (Total number of outcomes). It is used to measure the likelihood of a specific event occurring in a random selection scenario.
2
Two-Way Frequency Tables
A two-way frequency table displays categorical data by showing the frequency of two variables (here, gender and favourite hobby) in rows and columns. It is used to organize and analyze relationships between two sets of categorical data, and to quickly extract specific joint frequency values for probability calculations.
3
Fraction Simplification
Fraction simplification involves dividing both the numerator and denominator by their greatest common divisor (GCD) to reduce the fraction to its lowest terms. This makes the fraction easier to interpret and compare, and is a standard practice for presenting fractional probability results.
Loading solution...
