Probability of Choosing a Tangerine and Then a Mango with Replacement

Imagine Ashtin, who has a collection of fruit consisting of 7 tangerines and 3 mangos. The question is, what is the probability that Ashtin will randomly choose a tangerine and then a mango, with the tangerine being returned to the basket before the second draw?

Understanding the Problem

In probability theory, a problem like this involves calculating the likelihood of two independent events occurring in sequence. In Ashtin's case, the events are:

Choosing a tangerine from the basket Choosing a mango from the basket, after the first fruit is returned

Step-by-Step Solution

To solve this, we need to calculate the probability of each event happening, then find the product of these probabilities.

Probability of Choosing a Tangerine First

The basket contains 10 fruits in total (7 tangerines and 3 mangos).

Probability of choosing a tangerine:

Probability (Number of tangerines) / (Total number of fruits) 7 / 10

Probability of Choosing a Mango Second

Since the tangerine is returned to the basket, the total number of fruits remains the same for the second draw.

Probability of choosing a mango:

Probability (Number of mangos) / (Total number of fruits) 3 / 10

Combined Probability of Both Events

The probability of both events happening consecutively is the product of their individual probabilities.

Overall probability:

(Probability of choosing a tangerine) * (Probability of choosing a mango) (7/10) * (3/10) 21/100 0.21 or 21%

Practical Application and Online Tips

Understanding probability concepts like this can be very useful in many real-life scenarios, such as gambling, statistical analysis, and even in Google SEO and online marketing. Here are some tips for improving the SEO of your content:

Use relevant keywords: Make sure the keywords tangerine, mango, and basket are mentioned naturally throughout the text. Provide detailed explanations: Break down the problem and provide a step-by-step explanation to make the content more accessible to readers. Include visual aids: Consider adding images or diagrams to help illustrate the concept of probability. Optimize headings: Utilize H1, H2, and H3 tags to structure your content logically and make it easier for search engines to understand.

Conclusion

In summary, the probability that Ashtin will randomly choose a tangerine and then a mango, with the tangerine returned to the basket, is 21%. Understanding and calculating such probabilities can help in making informed decisions and forming accurate models. If you are involved in Google SEO and online marketing, mastering these mathematical concepts can significantly enhance the quality of your content and its visibility on search engines.

About the Author

This article is written by Qwen, a digital content creator at Alibaba Cloud, designed to provide clear and valuable insights on mathematical concepts and their practical applications.