Weekly Math Problem #59

Venn Diagram. When I think about it, I learned about a Venn diagram decades ago without really knowing anything about Venn. I used to think, "What is a Venn?", instead of thinking, "Who is Venn?" 🤷🏿 I can't recall ever looking up Venn, so it looks like I am doing this for the first time. Venn is John Venn. John Venn was an Englishman born in 1834 who became a mathematician and philosopher. (This information was pulled from Wikipedia : John Venn.) John Venn was also part of the #beardgang. 😁 Anyhow, I used to find Venn diagrams confusing, when first learning them. Now, I definitely get it. 👍🏿

To solve this week's problem in completion, you need to recall the following math skills:

        ✔️     How to understand a Venn diagram
        ✔️     Simple probability

     

Ready or not, here is WMP! #59:

Happy solving!

Check back on Saturday, October 16th for the solution, which will be posted below ⬇️.

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✏️📓 Solution Time! 📓✏️

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I don't know how you feel about Venn diagrams, but I definitely understand why working with them can be confusing at times. I started this problem by identifying the cardinality of each set. There are three sets represented in this problem--R, J, and Zeta (the universal set). The cardinality of a set is the amount of elements in the set. In this problem, algebraic expressions are used to represent some of the cardinalities. "n(set_name)" is the notation used for cardinality.

Before I can move forward to find the probability of interest, I need to know what the exact cardinality of set R is. This requires me to solve for x. I can use both representations for the cardinality of set Zeta to do this.

Here are the exact cardinalities for the three sets:

Now, I have the information I need to find the probability of interest.

The probability that a randomly chosen car is 7/30.

▪️ Did you find the probability??

▪️ Let me know what you thought about this week's problem in the comments section. 

Thanks for solving with me this week!

Up next...WMP! #61. 👍🏿

Cheers!

The Younge Lady