https://r2.erweima.ai/mathbot/image/1726048313516g8wxnuk3.jpg

HERE THE FREQEUNCE IUSN BETWEEN 1 AND -1 OR 0 AND 2 AND WHY

Let's go over the contents of the image first.

The problem describes a mouse population with:
- **50% females and 50% males**.
- The frequency of the albino trait is **\( p \) in males** and **20% in females**.

You are asked to calculate probabilities involving albino and male/female mice.

Now, the range of \( p \) can be derived from the fact that **probabilities** (like frequencies) should always be **between 0 and 1**. So the value of \( p \), which is the probability of a male being albino, must lie between **0 and 1**. This is because probabilities are always restricted to this interval in any real-world scenario.

This means \( p \in [0, 1] \), **not** between -1 and 1 or between 0 and 2.

Let me know if you'd like more detailed explanations on the specific parts of this problem, or if you'd like me to go step by step solving these probabilities!

### Expanding questions:
1. What is the total probability that a randomly chosen mouse is albino, combining both male and female probabilities?
2. How would the overall probability change if the percentage of females was not 50% but 60%?
3. How can we calculate the probability that a chosen mouse is either male or albino?
4. What approach can we use to determine the value of \( p \) such that the probability in part 4 of the question is less than or equal to 0.6?
5. How does the fact that we are drawing 5 mice simultaneously (in question 5) change the approach compared to selecting one mouse at a time?

**Tip:** Remember that when dealing with populations split into two groups (like males and females), the overall probability often involves combining the individual probabilities from each group, weighted by their respective proportions in the population.

We consider a mouse population with 50% female. It is assumed that the frequency of the albino trait is p in males and 20% in females. We choose a mouse at random. Calculate in terms of p the probability that:
1. The chosen mouse is male and albino.
2. The chosen mouse is albino.
3. The chosen mouse is male or albino.
4. The albino chosen is a male. Determine the value of p such that this probability is less or equal to 0.6.
5. 5 mice are drawn simultaneously from 100 mice with 30% albinos. Assume all have equal probability.

Explore a probability problem involving a mouse population with a 50% gender split and varying albino traits. Learn how to calculate the probability of randomly choosing an albino or male mouse, using core concepts like conditional probability and Bayes' Theorem.

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