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YW
Numerade Educator

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Problem 4 Easy Difficulty

Senate Partisanship The composition of the Senate of the 114th Congress is
$$
\text { 54 Republicans } \quad \text { 2 Independent } \quad 44 \text { Democrats }
$$
A new committee is being formed to study ways to benefit the arts in education. If 3 Senators are selected at random to form a new committee, what is the probability that they will all be Republicans? What is the probability that they will all be Democrats? What is the probability that there will be 1 from each party, including the Independent?

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Video Transcript

Now we have 54 Republicans, two independent and 44 Democrats in the Senate. And suppose we randomly select three senators. Two form a new community. We want to know the probable probability for the following three situations. And first, let's, um, compute the total number of people in the Senate. It is 54 plus two plus 44 and those equals 100. And then oops. Let's look at Part eight, where all three senators come from Republicans. Um, so probability of three Republicans. And this is easy because we wanna choose three out of 54 Republicans divided by the the number, the total number of choices of choosing three senators. So this should be 100. Choose three. And this equals these air. Quite large numbers. So we have to use calculator for this. Finally, the probability is 0.153 Okay, Next we want to know the probability of all three senators comes come from Democrats, and this is similar to part eight, and we want to choose three out of 44 Democrats divided by the total number of choices, which is 100 shoes three and we can recycle the value of the denominator from part A. And this equals 2.0, 82. And now, part C is a little bit different because we wanted select one from each party. So this is actually 33 steps, So one from each. Now we wanna first select one from the Republicans. This is 54. Choose one times, select one from independent. This is to choose one times. Um, so that one from Democrats for a fortunes one divided by Sorry. Ah, 100 shoes. Three The Sequels 54 times, two times 44 divided by the same denominator. And those equals 0.29 and we're done.