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:
The probability that at least one reaction will occur is 13/15 or approximately 0.867 (86.7%).
Explanation
This is a probability question involving a random selection from a group of items with different properties. We are given:
- 6 flasks in total:
- 2 flasks contain water (no reaction with yeast)
- 4 flasks contain hydrogen peroxide (reacts with yeast)
- Yeast is added to 2 flasks, chosen at random.
We are asked to find the probability that at least one reaction occurs, meaning at least one of the two flasks contains hydrogen peroxide.
Step 1: Total Ways to Choose 2 Flasks
From 6 flasks, the number of ways to choose 2 flasks is: (62)=6×52=15\binom{6}{2} = \frac{6 \times 5}{2} = 15
Step 2: Count Unfavorable Outcome (No Reaction)
The only way no reaction occurs is if both flasks chosen contain water.
- There are 2 water flasks, and the number of ways to choose both is:
(22)=1\binom{2}{2} = 1
So, only 1 out of the 15 possible selections results in no reaction.
Step 3: Use Complement Rule
We want the probability that at least one reaction occurs, which is the complement of no reaction: P(at least one reaction)=1−P(no reaction)P(\text{at least one reaction}) = 1 – P(\text{no reaction}) =1−115=1415= 1 – \frac{1}{15} = \frac{14}{15}
But this seems incorrect—wait!
Let’s correct this.
- Actually, the number of ways to choose 2 water flasks is 1
- So, number of ways that involve at least one hydrogen peroxide is:
15−1=1415 – 1 = 14
Therefore, the correct answer is 14/15, not 13/15.
✅ Final Correct Answer: 14/15 or about 93.3%
So, there is a 93.3% chance that at least one of the two flasks you add yeast to will contain hydrogen peroxide and produce a reaction.
