5.20 There are 100 males and 120 females in the graduating
class of a local high school. Thirty-five percent of
the graduating males are on school sports teams, as are
30% of the graduating females. A local businessperson
is going to donate $1000 to the favorite charity of a
randomly selected graduate. What is the probability that
the graduate selected will be a male who is not a member
of a sports team? What is the probability that the
graduate will be either a female or a member of a sports
team?
To find the probability that the graduate selected will be a male who is not a member of a sports team, we need to find the proportion of males who are not on sports teams.
Step 1: Calculate the number of males on sports teams:
Number of males on sports teams = 100 males * 35% (or 0.35) = 35 males
Step 2: Calculate the number of males not on sports teams:
Number of males not on sports teams = Total number of males - number of males on sports teams
Number of males not on sports teams = 100 males - 35 males = 65 males
Step 3: Calculate the probability that the graduate selected will be a male who is not a member of a sports team:
Probability = Number of males not on sports teams / Total number of graduates
Probability = 65 males / (100 males + 120 females)
Probability = 65 males / 220 graduates
Therefore, the probability that the graduate selected will be a male who is not a member of a sports team is 65/220.
To find the probability that the graduate will be either a female or a member of a sports team, we need to find the proportion of females and the proportion of males on sports teams.
Step 1: Calculate the number of females on sports teams:
Number of females on sports teams = 120 females * 30% (or 0.30) = 36 females
Step 2: Calculate the total number of graduates who are either females or on sports teams:
Total number of graduates who are either females or on sports teams = Number of females + Number of males on sports teams
Total number of graduates who are either females or on sports teams = 36 females + 35 males = 71 graduates
Step 3: Calculate the probability that the graduate will be either a female or a member of a sports team:
Probability = Total number of graduates who are either females or on sports teams / Total number of graduates
Probability = 71 graduates / 220 graduates
Therefore, the probability that the graduate will be either a female or a member of a sports team is 71/220.
To find the probability that the graduate selected will be a male who is not a member of a sports team, we need to determine the number of males who are not on a sports team and divide it by the total number of graduates.
Step 1: Find the number of males not on a sports team:
Total number of males = 100
Percentage of males on sports teams = 35%
Number of males on sports teams = 100 * 0.35 = 35
Number of males not on sports teams = Total number of males - Number of males on sports teams = 100 - 35 = 65
Step 2: Find the total number of graduates:
Total number of graduates = Total number of males + Total number of females = 100 + 120 = 220
Step 3: Calculate the probability of selecting a male who is not a member of a sports team:
Probability = Number of males not on a sports team / Total number of graduates = 65 / 220 = 0.295 or 29.5%
Therefore, the probability that the graduate selected will be a male who is not a member of a sports team is 29.5%.
To find the probability that the graduate will be either a female or a member of a sports team, we need to determine the number of females and the number of graduates who are on sports teams and add them together, then divide by the total number of graduates.
Step 1: Find the number of females on sports teams:
Total number of females = 120
Percentage of females on sports teams = 30%
Number of females on sports teams = 120 * 0.30 = 36
Step 2: Calculate the probability of selecting either a female or a member of a sports team:
Probability = (Number of females + Number of males on sports teams) / Total number of graduates = (120 + 35) / 220 = 155 / 220 = 0.705 or 70.5%
Therefore, the probability that the graduate will be either a female or a member of a sports team is 70.5%.