Three molecules of type a , two of type ß, one of type y, and four of type 7 are to be linked together to form a chain molecule. One such chain molecule is aßynaßnamn. Please answer the following questions. ) How many such chain molecules are there? i) Suppose a chain molecule of the type described above is randomly selected. What is the probability that all three molecules of each type end up next to one another ( an example of such a chain molecule is aaaßßynmnn
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
![### Chain Molecule Configuration
#### Problem Statement:
Three molecules of type \( \alpha \), two of type \( \beta \), one of type \( \gamma \), and four of type \( \eta \) are to be linked together to form a chain molecule. One such chain molecule is \( \alpha \beta \gamma \eta \alpha \beta \eta \eta \eta \). Please answer the following questions:
#### Questions:
i) **How many such chain molecules are there?**
ii) **Suppose a chain molecule of the type described above is randomly selected. What is the probability that all three molecules of each type end up next to one another?** (An example of such a chain molecule is \( \alpha \alpha \alpha \beta \beta \gamma \eta \eta \eta \eta \)).
#### Graphs/Diagrams:
There are no graphs or diagrams in the provided image. The explanation included is textual and involves combinatorial and probabilistic analysis of chain molecules.
**Explanation:**
- The problem requires determining the number of chain molecule configurations that can be formed given the specific constraints on molecule types.
- Additionally, the problem asks for the probability of a specific arrangement where molecules of each type are adjacent to each other.
For further detailed solutions, combinatorial formulas and probability concepts will need to be applied.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F00a48d79-f805-418c-a679-1c91878d1d75%2F154c46a4-c1e7-4589-9465-299387f6efcb%2Fmxdd5xt_processed.png&w=3840&q=75)
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