We are given a
probability tree diagram and asked:
>
What is the probability of winning two games in a row?
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Step 1: Understand the Tree Diagram
The tree shows the outcomes of
two sequential games, where each game has two possible outcomes:
-
Win (with probability 0.4)
-
Not win (with probability 0.6)
The first branch represents the outcome of
Game 1:
- Win → probability 0.4
- Not win → probability 0.6
From each of those, we branch again for
Game 2:
- If Game 1 was a
win, then Game 2:
- Win → 0.4
- Not win → 0.6
- If Game 1 was
not win, then Game 2:
- Win → 0.4
- Not win → 0.6
So the structure is independent — the outcome of Game 2 does not depend on Game 1. Each game has a
0.4 chance of winning, regardless of prior results.
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Step 2: Find the Probability of Winning Two Games in a Row
This means:
Win Game 1 AND Win Game 2
Since the games are independent (as shown by the tree — same probabilities branching from both “win” and “not win”), we multiply the probabilities:
> P(Win Game 1) × P(Win Game 2) = 0.4 × 0.4 =
0.16
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Step 3: Match with Answer Choices
A) 1.6
B) 0.8
C) 0.25
D)
0.16 ✔
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✔ Final Answer: D) 0.16
This is the correct probability of winning two games in a row.
Parent Tip: Review the logic above to help your child master the concept of probability trees worksheet.
