Math Problem Statement
Реши тази задача
Solution
This problem involves finding the probability of drawing two balls of the same color from a box containing 6 white balls and 4 black balls.
Total number of balls
The total number of balls is:
Total ways to choose 2 balls
The total number of ways to choose 2 balls from 10 is calculated using the combination formula: Here:
Ways to choose 2 balls of the same color
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Two white balls:
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Two black balls:
Total favorable outcomes
The total number of favorable outcomes (same color) is:
Probability
The probability of drawing two balls of the same color is:
Simplify the fraction:
Final Answer:
The probability of drawing two balls of the same color is:
Would you like a step-by-step explanation of how the formula works or further assistance with similar problems?
Here are five related questions for practice:
- What is the probability of drawing two balls of different colors?
- If one ball is replaced after each draw, how would the probabilities change?
- What is the probability of drawing at least one white ball in two draws?
- How does the probability change if there are 5 white and 5 black balls instead?
- How can we calculate the probability of drawing three balls of the same color in a similar problem?
Tip: Always ensure the total number of combinations is calculated correctly when working with probability problems.
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Math Problem Analysis
Mathematical Concepts
Combinatorics
Probability
Formulas
C(n, k) = n! / (k!(n-k)!)
Probability = Favorable Outcomes / Total Outcomes
Theorems
Basic Probability Theorem
Suitable Grade Level
Grades 8-10
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