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 12 red balls and 5 blue balls.
Drawing One ball With replacement.
Drawing One ball With replacement.
Question: What is the probability of drawing a blue ball?
Explanation:
Solution – Probability With replacement:
Given:
• Red balls: 12
• Blue balls: 5
• Total: 17
• Number of draws: 1
Basic probabilities:
\(P(\text{Red}) = \frac{12}{17}\)
\(P(\text{Blue}) = \frac{5}{17}\)
Probability tree:
Answer:: \(\frac{5}{17}\)
Given:
• Red balls: 12
• Blue balls: 5
• Total: 17
• Number of draws: 1
Basic probabilities:
\(P(\text{Red}) = \frac{12}{17}\)
\(P(\text{Blue}) = \frac{5}{17}\)
Probability tree:
Answer:: \(\frac{5}{17}\)
Example 2
🎲 Probability - With replacement:
A bag contains 11 red balls and 10 blue balls.
Drawing One ball With replacement.
Drawing One ball With replacement.
Question: What is the probability of drawing a blue ball?
Explanation:
Solution – Probability With replacement:
Given:
• Red balls: 11
• Blue balls: 10
• Total: 21
• Number of draws: 1
Basic probabilities:
\(P(\text{Red}) = \frac{11}{21}\)
\(P(\text{Blue}) = \frac{10}{21}\)
Probability tree:
Answer:: \(\frac{10}{21}\)
Given:
• Red balls: 11
• Blue balls: 10
• Total: 21
• Number of draws: 1
Basic probabilities:
\(P(\text{Red}) = \frac{11}{21}\)
\(P(\text{Blue}) = \frac{10}{21}\)
Probability tree:
Answer:: \(\frac{10}{21}\)
Example 3
🎲 Probability - With replacement:
A bag contains 11 red balls and 10 blue balls.
Drawing One ball With replacement.
Drawing One ball With replacement.
Question: What is the probability of drawing a blue ball?
Explanation:
Solution – Probability With replacement:
Given:
• Red balls: 11
• Blue balls: 10
• Total: 21
• Number of draws: 1
Basic probabilities:
\(P(\text{Red}) = \frac{11}{21}\)
\(P(\text{Blue}) = \frac{10}{21}\)
Probability tree:
Answer:: \(\frac{10}{21}\)
Given:
• Red balls: 11
• Blue balls: 10
• Total: 21
• Number of draws: 1
Basic probabilities:
\(P(\text{Red}) = \frac{11}{21}\)
\(P(\text{Blue}) = \frac{10}{21}\)
Probability tree:
Answer:: \(\frac{10}{21}\)
Practice
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