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Probability of Not Choosing a Blue Ball from a Bag
Mathematics
Junior High School (Grade 7-8)
Question Content
A bag contains 4 red balls, 3 blue balls, and 5 green balls. If one ball is chosen at random, what is the probability that it is not blue? \nA) \( \frac{1}{4} \) \nB) \( \frac{3}{4} \) \nC) \( \frac{2}{3} \) \nD) \( \frac{5}{12} \)
Correct Answer
3/4
Detailed Solution Steps
1
Step 1: Calculate the total number of balls in the bag. Add the number of red, blue, and green balls: \( 4 + 3 + 5 = 12 \) total balls.
2
Step 2: Determine the number of non - blue balls. Subtract the number of blue balls from the total, or add red and green: \( 4 + 5 = 9 \) non - blue balls.
3
Step 3: Recall the probability formula: \( P(\text{event})=\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \). For the event of 'not blue', the favorable outcomes are 9, and total outcomes are 12.
4
Step 4: Simplify the fraction \( \frac{9}{12} \) by dividing numerator and denominator by their greatest common divisor (3): \( \frac{9\div3}{12\div3}=\frac{3}{4} \).
Knowledge Points Involved
1
Probability of an Event
Probability measures the likelihood of an event occurring, calculated as \( P(E)=\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \). It is used to analyze random events, like choosing a ball from a bag, and ranges from 0 (impossible) to 1 (certain).
2
Total and Favorable Outcomes in Probability
Total outcomes are all possible results of an experiment (e.g., all balls in the bag). Favorable outcomes are the results that satisfy the event (e.g., non - blue balls). Identifying these is essential to apply the probability formula correctly.
3
Simplifying Fractions
Simplifying a fraction involves dividing the numerator and denominator by their greatest common divisor (GCD) to reduce the fraction to its lowest terms (e.g., \( \frac{9}{12} \) simplifies to \( \frac{3}{4} \) by dividing both by 3). This is important for presenting probability in a clear, simplified form.
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