Practice Probability with Tree Diagrams
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Unlimited problems
Full explanations
P(event) = favourable outcomes ÷ total outcomes
- AND: multiply probabilities along a branch
- OR: add probabilities of separate branches
Worked Examples
Example 1
🎲 Probability - With replacement:
A bag contains 1 red balls and 8 blue balls.
Drawing One ball With replacement.
Drawing One ball With replacement.
Question: What is the probability of drawing a red ball?
Explanation:
Solution – Probability With replacement:
Given:
• Red balls: 1
• Blue balls: 8
• Total: 9
• Number of draws: 1
Basic probabilities:
\(P(\text{Red}) = \frac{1}{9}\)
\(P(\text{Blue}) = \frac{8}{9}\)
Probability tree:
Answer:: \(\frac{1}{9}\)
Given:
• Red balls: 1
• Blue balls: 8
• Total: 9
• Number of draws: 1
Basic probabilities:
\(P(\text{Red}) = \frac{1}{9}\)
\(P(\text{Blue}) = \frac{8}{9}\)
Probability tree:
Answer:: \(\frac{1}{9}\)
Example 2
🎲 Probability - With replacement:
A bag contains 12 red balls and 1 blue balls.
Drawing One ball With replacement.
Drawing One ball With replacement.
Question: What is the probability of drawing a red ball?
Explanation:
Solution – Probability With replacement:
Given:
• Red balls: 12
• Blue balls: 1
• Total: 13
• Number of draws: 1
Basic probabilities:
\(P(\text{Red}) = \frac{12}{13}\)
\(P(\text{Blue}) = \frac{1}{13}\)
Probability tree:
Answer:: \(\frac{12}{13}\)
Given:
• Red balls: 12
• Blue balls: 1
• Total: 13
• Number of draws: 1
Basic probabilities:
\(P(\text{Red}) = \frac{12}{13}\)
\(P(\text{Blue}) = \frac{1}{13}\)
Probability tree:
Answer:: \(\frac{12}{13}\)
Example 3
🎲 Probability - With replacement:
A bag contains 12 red balls and 1 blue balls.
Drawing One ball With replacement.
Drawing One ball With replacement.
Question: What is the probability of drawing a red ball?
Explanation:
Solution – Probability With replacement:
Given:
• Red balls: 12
• Blue balls: 1
• Total: 13
• Number of draws: 1
Basic probabilities:
\(P(\text{Red}) = \frac{12}{13}\)
\(P(\text{Blue}) = \frac{1}{13}\)
Probability tree:
Answer:: \(\frac{12}{13}\)
Given:
• Red balls: 12
• Blue balls: 1
• Total: 13
• Number of draws: 1
Basic probabilities:
\(P(\text{Red}) = \frac{12}{13}\)
\(P(\text{Blue}) = \frac{1}{13}\)
Probability tree:
Answer:: \(\frac{12}{13}\)
Practice
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