Question

The table below gives the political party affiliation and the self-described political orientation from a random sample of 1866 U.S. adults.

	Democrat	Republican	Other Parties	Total
Liberal	300	42	160	502
Moderate	256	120	333	709
Conservative	147	345	163	655
Total	703	507	656	1866

Find the following probabilities: Show the fraction work and round answers to 3 decimal places.

a) P(Other Parties and Conservative)

b) P(Democrat or Republican)

c) P(Republican or Conservative)

d) P(Democrat | Moderate)

Answer 1

From given table we find the following probabilities,

a) P(Other Parties and Conservative) = 163 / 1866 = 0.087

=> P(Other Parties and Conservative) = 0.087

b) P(Democrat or Republican)

= P(Democrat) + P(Republican) - P(Democrat and Republican)

= (703 / 1866) + (507 / 1866) - 0

= (703 + 507) / 1866

= 1210 / 1866

= 0.648

=> P(Democrat or Republican) = 0.648

c) P(Republican or Conservative)

= P(Republican) + P(Conservative) - P(Republican and Conservative)

= (507 / 1866) + (655 / 1866) - (345 / 1866)

= (507 + 655 - 345) / 1866

= 817 / 1866

= 0.438

=> P(Republican or Conservative) = 0.438

d) P(Democrat | Moderate) = 256 / 709 = 0.361

=> P(Democrat | Moderate) = 0.361