Question

Suppose we are selecting a group of representatives from the 110th US Senate. In this year, there were 49 Republicans and 51 Democrats*. Use this information to answer the following.

*Technically, 2 of these Senators were Independents or Independent Democrats, but caucused with the Democratic Party.
Remember the rounding convention for a decimal value with more than 3 zeroes is to round to the second non-zero digit.

Step 1 of 6: If we choose a committee of 12 at random, what is the probability that they will all be Republicans?

Step 2 of 6: If we choose a committee of 12 at random, what is the probability that the committee will contain all Democrats (for this question, do not separate out the Independent Senators)?

Step 3 of 6: If we choose a committee of 12 at random, what is the probability that the committee will contain all Democrats (for this question, DOseparate out the Independent Senators)?

Step 4 of 6: If we choose a committee of 12 at random, what is the probability that the committee will contain exactly half Democrats (for this question, do not separate out the Independent Senators) and half Republicans?

Step 5 of 6: Interpret your probability from the previous step.

Step 6 of 6: Using your previous answers, which, if any of the committees discussed would be unusual?

Answer 1

5) the probability computed in step 4 is 0.24 ie, 24% of the times the committee will have half republicans and half democrats.

6) the committees discussed in step 1,2 and 3 will be very unsual as their probabilities are very low(almost equal to 0). the committee discussed in step 4 is not as unusual as the probability is not equal to 0.