Casting Lots on Yom Kippur

Please read through the sources below and consider the following questions:

1. What do they all have in common?

2. What is different among these different situations/rituals?

3. Based on these passages, why do you think Chazal make a comparison between Yom Kippur and Purim?

(ז) וְלָקַ֖ח אֶת־שְׁנֵ֣י הַשְּׂעִירִ֑ם וְהֶעֱמִ֤יד אֹתָם֙ לִפְנֵ֣י יְהוָ֔ה פֶּ֖תַח אֹ֥הֶל מוֹעֵֽד׃ (ח) וְנָתַ֧ן אַהֲרֹ֛ן עַל־שְׁנֵ֥י הַשְּׂעִירִ֖ם גּוֹרָל֑וֹת גּוֹרָ֤ל אֶחָד֙ לַיהוָ֔ה וְגוֹרָ֥ל אֶחָ֖ד לַעֲזָאזֵֽל׃ (ט) וְהִקְרִ֤יב אַהֲרֹן֙ אֶת־הַשָּׂעִ֔יר אֲשֶׁ֨ר עָלָ֥ה עָלָ֛יו הַגּוֹרָ֖ל לַיהוָ֑ה וְעָשָׂ֖הוּ חַטָּֽאת׃ (י) וְהַשָּׂעִ֗יר אֲשֶׁר֩ עָלָ֨ה עָלָ֤יו הַגּוֹרָל֙ לַעֲזָאזֵ֔ל יָֽעֳמַד־חַ֛י לִפְנֵ֥י יְהוָ֖ה לְכַפֵּ֣ר עָלָ֑יו לְשַׁלַּ֥ח אֹת֛וֹ לַעֲזָאזֵ֖ל הַמִּדְבָּֽרָה׃
(7) Aaron shall take the two he-goats and let them stand before the LORD at the entrance of the Tent of Meeting; (8) and he shall place lots upon the two goats, one marked for the LORD and the other marked for Azazel. (9) Aaron shall bring forward the goat designated by lot for the LORD, which he is to offer as a sin offering; (10) while the goat designated by lot for Azazel shall be left standing alive before the LORD, to make expiation with it and to send it off to the wilderness for Azazel.
(ז) וַיֹּאמְר֞וּ אִ֣ישׁ אֶל־רֵעֵ֗הוּ לְכוּ֙ וְנַפִּ֣ילָה גֽוֹרָל֔וֹת וְנֵ֣דְעָ֔ה בְּשֶׁלְּמִ֛י הָרָעָ֥ה הַזֹּ֖את לָ֑נוּ וַיַּפִּ֙לוּ֙ גּֽוֹרָל֔וֹת וַיִּפֹּ֥ל הַגּוֹרָ֖ל עַל־יוֹנָֽה׃ (ח) וַיֹּאמְר֣וּ אֵלָ֔יו הַגִּידָה־נָּ֣א לָ֔נוּ בַּאֲשֶׁ֛ר לְמִי־הָרָעָ֥ה הַזֹּ֖את לָ֑נוּ מַה־מְּלַאכְתְּךָ֙ וּמֵאַ֣יִן תָּב֔וֹא מָ֣ה אַרְצֶ֔ךָ וְאֵֽי־מִזֶּ֥ה עַ֖ם אָֽתָּה׃ (ט) וַיֹּ֥אמֶר אֲלֵיהֶ֖ם עִבְרִ֣י אָנֹ֑כִי וְאֶת־יְהוָ֞ה אֱלֹהֵ֤י הַשָּׁמַ֙יִם֙ אֲנִ֣י יָרֵ֔א אֲשֶׁר־עָשָׂ֥ה אֶת־הַיָּ֖ם וְאֶת־הַיַּבָּשָֽׁה׃
(7) The men said to one another, “Let us cast lots and find out on whose account this misfortune has come upon us.” They cast lots and the lot fell on Jonah. (8) They said to him, “Tell us, you who have brought this misfortune upon us, what is your business? Where have you come from? What is your country, and of what people are you?” (9) “I am a Hebrew,” he replied. “I worship the LORD, the God of Heaven, who made both sea and land.”
(ו) וַיִּ֣בֶז בְּעֵינָ֗יו לִשְׁלֹ֤ח יָד֙ בְּמָרְדֳּכַ֣י לְבַדּ֔וֹ כִּֽי־הִגִּ֥ידוּ ל֖וֹ אֶת־עַ֣ם מָרְדֳּכָ֑י וַיְבַקֵּ֣שׁ הָמָ֗ן לְהַשְׁמִ֧יד אֶת־כָּל־הַיְּהוּדִ֛ים אֲשֶׁ֛ר בְּכָל־מַלְכ֥וּת אֲחַשְׁוֵר֖וֹשׁ עַ֥ם מָרְדֳּכָֽי׃ (ז) בַּחֹ֤דֶשׁ הָרִאשׁוֹן֙ הוּא־חֹ֣דֶשׁ נִיסָ֔ן בִּשְׁנַת֙ שְׁתֵּ֣ים עֶשְׂרֵ֔ה לַמֶּ֖לֶךְ אֲחַשְׁוֵר֑וֹשׁ הִפִּ֣יל פּוּר֩ ה֨וּא הַגּוֹרָ֜ל לִפְנֵ֣י הָמָ֗ן מִיּ֧וֹם ׀ לְי֛וֹם וּמֵחֹ֛דֶשׁ לְחֹ֥דֶשׁ שְׁנֵים־עָשָׂ֖ר הוּא־חֹ֥דֶשׁ אֲדָֽר׃ (ס)
(6) But he disdained to lay hands on Mordecai alone; having been told who Mordecai’s people were, Haman plotted to do away with all the Jews, Mordecai’s people, throughout the kingdom of Ahasuerus. (7) In the first month, that is, the month of Nisan, in the twelfth year of King Ahasuerus, pur—which means “the lot”—was cast before Haman concerning every day and every month, [until it fell on] the twelfth month, that is, the month of Adar.

Let's take a deeper look at this theme of casting lots. It is clearly a central theme of Yom Kippur, as it appears in two of the readings, and it also underlies the connection between Purim and Yom Kippur.

Please follow the links to several articles about this idea of "casting lots" and fill in the chart below:

Aish.com "Scapegoat"

http://www.aish.com/h/hh/yom-kippur/theme/102720984.html

Chabad.org "The Angel and the Drunk"

http://www.chabad.org/library/article_cdo/aid/2549/jewish/The-Angel-and-the-Drunk.htm

Ou.org "Puim and YK: An Odd Couple?

https://www.ou.org/holidays/purim/purim_and_yom_kippur/

Main points of the article (pick 3-5...what is casting lots all about? what is the connection to Purim? etc.)
According to the article, why is this an appropriate theme for YK?