A. The probability of selecting a Texas high school coach who belongs to ONLY TISCA can be calculated by subtracting the percentage of coaches belonging to both associations from the percentage of coaches belonging to TISCA.
88% of coaches belong to TISCA
6% of coaches belong to BOTH associations
So, the probability of selecting a coach belonging ONLY to TISCA is:
88% - 6% = 82%
B. The probability of selecting a Texas high school coach who belongs to both NISCA and TISCA can be determined directly from the information given.
6% of coaches belong to BOTH associations
Therefore, the probability of selecting a coach who belongs to BOTH associations is:
6%
C. The probability of selecting a Texas high school coach who belongs to neither association can be calculated by finding the complement of the total percentage of coaches who belong to at least one association.
15% of coaches belong to NISCA
88% of coaches belong to TISCA
6% of coaches belong to BOTH associations
So, the probability of selecting a coach who belongs to NEITHER association is:
100% - (15% + 88% - 6%) = 3%
D. The probability of selecting a Texas high school coach who belongs to ONLY ONE of the two associations can be found by summing the probabilities of selecting a coach who belongs ONLY to NISCA and the probability of selecting a coach who belongs ONLY to TISCA.
6% of coaches belong to NISCA ONLY
82% of coaches belong to TISCA ONLY (as calculated in part A)
Thus, the probability of selecting a coach who belongs to ONLY ONE of the two associations is:
6% + 82% = 88%
