During the 2016 presidential campaign, Hillary Clinton tweeted the following about background checks for gun ownership. It is an example of the wrong use of Venn diagrams and not using conditional probabilities.

a. Define the two events \(\mathrm{A}=\{\) gun owner \(\}\) and \(\mathrm{B}=\) \{support background checks\} for a randomly selected American adult. Draw a correct Venn diagram (without including any percentages) that conveys the message that most gun owners support universal background checks.

b. According to polls, \({ }^{10} 43 \%\) of Americans personally own guns. Of those personally owning guns, \(87 \%\) favor universal background checks. Based on these numbers, state \(\mathrm{P}(\mathrm{A})\) and \(\mathrm{P}(\mathrm{B} \mid \mathrm{A})\) and create a tweet (at most 280 characters) that describes these findings.
c. The polls also showed that overall, \(93 \%\) of Americans favor universal background checks. Use this information and the information from part \(b\) to find \(\mathrm{P}\left(\mathrm{B} \mid \mathrm{A}^{\mathrm{C}}\right)\). In words, what does this conditional probability tell us?
d. Think of a better display than the one used by Hillary Clinton to compare conditional probabilities of favoring background checks for gun owners and for those who don't own guns.

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90% of Americans Support universal background checks 83% of gun owners Hillary Clinton @HilaryClinton Dear Congress, Let's get this done. Thanks, The vast majority of Americans 11:21 AM-May 20, 2016 5,775 3,686 people are talking about this