15% of Texas high school swim coaches belong to NISCA (National Interscolastic Swim
Coaches Association). 88% of Texas high school swim coaches
belong to TISCA (Texas
Interscholastic Swim Coaches Association). 6% of Texas
high school swim coaches
belong to NISCA ONLY.
(Report as a percentage with no % sign)
A. What is the probability of selecting a Texas high school coach who belongs to ONLY
TISCA?
%
B. What is the probability of selecting a Texas high school coach who belongs to both?
%
C. What is the probability of selecting a Texas high school coach who belongs to neither?
%
D. What is the probability of selecting a Texas high school coach who belongs to ONLY
ONE of the two?
%

Question

kayleeesparza2006 kayleeesparza2006

02-05-2024
Mathematics

Answered

15% of Texas high school swim coaches belong to NISCA (National Interscolastic Swim
Coaches Association). 88% of Texas high school swim coaches
belong to TISCA (Texas
Interscholastic Swim Coaches Association). 6% of Texas
high school swim coaches
belong to NISCA ONLY.
(Report as a percentage with no % sign)
A. What is the probability of selecting a Texas high school coach who belongs to ONLY
TISCA?
%
B. What is the probability of selecting a Texas high school coach who belongs to both?
%
C. What is the probability of selecting a Texas high school coach who belongs to neither?
%
D. What is the probability of selecting a Texas high school coach who belongs to ONLY
ONE of the two?
%

Answer :

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GinnyAnswer GinnyAnswer · Answer 1 · 2024-05-02T16:36:06-04:00

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%