1. Total number of flasks: 6
2. Flasks containing hydrogen peroxide: 4
3. Flasks containing water: 2
   You are adding yeast to two of the flasks. We need to find the probability that at least one of these two flasks contains hydrogen peroxide.

Step-by-step calculation:

1. Total ways to choose 2 flasks out of 6:
   \[\binom { 6} { 2} = \frac { 6! } { 2! ( 6- 2) ! } = 15\]
2. Ways to choose 2 flasks that do not contain hydrogen peroxide (both containing water):
   \[\binom { 2} { 2} = 1\]
3. Ways to choose 2 flasks that contain hydrogen peroxide (both containing hydrogen peroxide):
   \[\binom { 4} { 2} = 6\]
4. Ways to choose 1 flask with water and 1 flask with hydrogen peroxide:
   \[\binom { 2} { 1} \times \binom { 4} { 1} = 2 \times 4 = 8\]
   So, the total number of favorable outcomes (at least one flask with hydrogen peroxide) is:
   \[6 + 8 = 14\]
   Therefore, the probability that at least one reaction will occur

Supplemental Knowledge

Probability is the measure of the likelihood that an event will occur. It ranges from 0 (impossible event) to 1 (certain event). When dealing with multiple events, it's important to understand the concepts of independent and dependent events, as well as complementary events.

1. Basic Probability Formula:
   • Probability of an event \(A\): \(P( A) = \frac { \text { Number of favorable outcomes} } { \text { Total number of possible outcomes} } \)
2. Complementary Events:
   • The probability that at least one event occurs can be found by calculating the probability that none of the events occur and subtracting it from 1.
   • Formula: \(P( \text { at least one} ) = 1 - P( \text { none} ) \)

Applied Knowledge

• Understanding probability helps in making informed decisions in daily life, such as assessing risks and benefits in scenarios like weather forecasting, insurance policies, and even playing games.

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