A. To find the probability of selecting a person who likes both teams, we need to subtract the percentage of people who like only one team from the total percentage who like the Cowboys and/or the Texans.
78% of people like the Cowboys, 57% like the Texans, and 14% like ONLY the Texans. To find the percentage of people who like both teams, we can add the percentage of people who like the Cowboys and the percentage who like the Texans, and then subtract the percentage who like ONLY the Texans:
78% (Cowboys) + 57% (Texans) - 14% (ONLY Texans) = 121% - 14% = 107%
Therefore, the probability of selecting a person who likes both teams is 107%.
B. To find the probability of selecting a person who likes neither team, we subtract the total percentage of people who like at least one team from 100%:
100% - (78% Cowboys + 57% Texans) = 100% - 135% = -35%
Since a negative probability doesn't make sense, it means that there might be a mistake in the provided information or calculations.
C. To find the probability of selecting a person who likes only the Cowboys, we can subtract the percentage of people who like both teams and those who like ONLY the Texans from the percentage who like the Cowboys:
78% (Cowboys) - 14% (ONLY Texans) = 64%
Therefore, the probability of selecting a person who likes only the Cowboys is 64%.
D. The probability of selecting a person who likes ONLY ONE team includes those who like only the Cowboys and those who like only the Texans. This can be calculated by adding the percentages of people who like only one team:
14% (ONLY Texans) + 64% (ONLY Cowboys) = 78%
Therefore, the probability of selecting a person who likes only one team is 78%.
