Your science teacher sets up six flasks. Two of the flasks contain water and four of the flasks contain hydrogen peroxide. A reaction occurs when you add yeast to hydrogen peroxide. You add yeast to two of the flasks. What is the probability that at least one reaction will occur?
Your science teacher sets up six flasks. Two of the flasks contain water and four of the flasks contain hydrogen peroxide. A reaction occurs when you add yeast to hydrogen peroxide. You add yeast to two of the flasks. What is the probability that at least one reaction will occur?
The Correct Answer and Explanation is:
✅ Correct Answer:
Probability = 13/15 or approximately 0.8667 (86.67%)
🧪 Explanation (Approximately 300 words):
To solve this problem, we are dealing with a probability scenario involving a favorable outcome: at least one reaction occurs when yeast is added to two randomly selected flasks out of six. Let’s break it down:
🔢 Step 1: Understand the setup
- Total number of flasks: 6
- Flasks with water (no reaction): 2
- Flasks with hydrogen peroxide (reaction with yeast): 4
- Yeast is added to 2 of the 6 flasks
🎯 Goal
We want to calculate the probability that at least one of the two chosen flasks contains hydrogen peroxide (i.e., at least one reaction occurs).
Instead of calculating this directly, we use the complement rule:
\text{P(at least one reaction)} = 1 – \text{P(no reaction)}
]
❌ Step 2: Calculate P(no reaction)
This happens only if both chosen flasks contain water, since yeast + water = no reaction.
- Number of ways to choose 2 flasks with only water: (22)=1\binom{2}{2} = 1
- Total number of ways to choose any 2 flasks out of 6: (62)=15\binom{6}{2} = 15
- So, P(no reaction)=115\text{P(no reaction)} = \frac{1}{15}
✅ Step 3: Use Complement Rule
P(at least one reaction)=1−115=1415\text{P(at least one reaction)} = 1 – \frac{1}{15} = \frac{14}{15}
⛔ Wait! Correction: Earlier we said 13/15—but upon rechecking:
If only 1 way out of 15 gives no reaction, then 14 ways give at least one reaction.
So the correct answer is:
\boxed{\frac{14}{15} \text{ or } 0.9333 \text{ or } 93.33%}
]
✅ Final Answer:
14/15 or about 93.33%
🧠 This means it’s very likely (93.33%) that you’ll see at least one reaction when you randomly add yeast to two of the flasks.
