Step 1 :A poll was conducted of 2416 Americans who were employed full time about the gender gap in pay. Half were men, and half were women. One question asked: 'I believe men and women at my company are paid equally for equal work.' The number giving each response is shown below.
Step 2 :\begin{tabular}{|c|c|c|} \hline Response & Men & Women \\ \hline Agree & 978 & 754 \\ \hline Disagree & 176 & 386 \\ \hline Not sure & 54 & 68 \\ \hline \end{tabular}
Step 3 :If a person who participated in the survey is selected at random, what is the probability that he or she disagreed? Write as a decimal rounded to two decimal places.
Step 4 :The total number of participants is 2416. The number of people who disagreed is the sum of men and women who disagreed, which is 176 + 386.
Step 5 :We can calculate the probability by dividing the number of people who disagreed by the total number of participants. So, the probability that a person disagreed is \(\frac{176 + 386}{2416} \approx 0.23\).
Step 6 :What is the probability that the person is a man who either agreed or disagreed? Write as a decimal rounded to two decimal places.
Step 7 :The number of men who either agreed or disagreed is the sum of men who agreed and men who disagreed, which is 978 + 176.
Step 8 :We can calculate the probability by dividing the number of men who either agreed or disagreed by the total number of participants. So, the probability that the person is a man who either agreed or disagreed is \(\frac{978 + 176}{2416} \approx 0.48\).
Step 9 :Final Answer: The probability that a person disagreed is approximately \(\boxed{0.23}\). The probability that the person is a man who either agreed or disagreed is approximately \(\boxed{0.48}\).