At a particular school with 200 male students, 58-play football, 40-play basketball, and 8 play both. What is
the probability that a randomly selected male student plays
a) At least one sport
b) Neither sport
c) Only basketball
40 - 8 = 32 only basketball
58 - 8 = 50 only football
32 + 50 + 8 = 90 some sport (answer A)
200 - 90 = 110 = no sport at all (B)
did only basketball up top
58+40-8 = 90
(a) 90/200
(b) 110/200
(c) (40-8)/200
a) The probability that a randomly selected male student plays at least one sport can be found by adding the probabilities of playing football, playing basketball, and subtracting the probability of playing both sports.
Probability of playing football = 58/200 = 0.29
Probability of playing basketball = 40/200 = 0.20
Probability of playing both sports = 8/200 = 0.04
Therefore, the probability of playing at least one sport is:
0.29 + 0.20 - 0.04 = 0.45 or 45%
b) The probability of a male student playing neither sport can be found by subtracting the probability of playing at least one sport from 1.
Probability of playing neither sport = 1 - Probability of playing at least one sport
= 1 - 0.45
= 0.55 or 55%
c) The probability of a male student playing only basketball can be found by subtracting the probability of playing both sports from the probability of playing basketball.
Probability of playing only basketball = Probability of playing basketball - Probability of playing both sports
= 0.20 - 0.04
= 0.16 or 16%
To calculate the probabilities, we need to use the principle of inclusion-exclusion.
a) To find the probability that a randomly selected male student plays at least one sport, we need to find the number of male students who play football, basketball, or both.
Number of male students who play football = 58
Number of male students who play basketball = 40
Number of male students who play both football and basketball = 8
Now, to find the number of male students who play at least one sport, we need to add the number of male students who play football and the number of male students who play basketball. However, we need to subtract the number of male students who play both football and basketball, since they were counted twice.
Number of male students who play at least one sport = (Number of male students who play football) + (Number of male students who play basketball) - (Number of male students who play both football and basketball)
= 58 + 40 - 8
= 90
So, the number of male students who play at least one sport is 90.
The total number of male students is 200.
Therefore, the probability that a randomly selected male student plays at least one sport is:
Probability (playing at least one sport) = (Number of male students who play at least one sport) / (Total number of male students)
= 90 / 200
= 0.45, or 45%
b) To find the probability that a randomly selected male student plays neither sport, we need to subtract the probability of playing at least one sport from 1.
Probability (playing neither sport) = 1 - Probability (playing at least one sport)
= 1 - 0.45
= 0.55, or 55%
So, the probability that a randomly selected male student plays neither sport is 0.55, or 55%.
c) To find the probability that a randomly selected male student plays only basketball, we need to subtract the number of male students who play both sports from the number of male students who play basketball only.
Number of male students who play basketball only = (Number of male students who play basketball) - (Number of male students who play both football and basketball)
= 40 - 8
= 32
Probability (playing only basketball) = (Number of male students who play only basketball) / (Total number of male students)
= 32 / 200
= 0.16, or 16%
So, the probability that a randomly selected male student plays only basketball is 0.16, or 16%.
To find the probabilities, we need to calculate the number of students who play each sport and the number of students who play both sports.
Let's solve the problem using a Venn diagram.
a) Probability of playing at least one sport:
To find the probability that a randomly selected male student plays at least one sport, we need to calculate the number of students who play at least one sport (football or basketball) divided by the total number of male students.
1. Find the number of students who play at least one sport:
- Number of students playing football = 58
- Number of students playing basketball = 40
- Number of students playing both sports = 8
- Total students who play at least one sport (football or basketball) = (number of students playing football) + (number of students playing basketball) - (number of students playing both sports)
= 58 + 40 - 8 = 90
2. Find the probability:
- Probability = (number of students who play at least one sport) / (total number of male students)
= 90 / 200
= 0.45 or 45%
b) Probability of playing neither sport:
To find the probability that a randomly selected male student plays neither sport, we need to calculate the number of students who play neither sport divided by the total number of male students.
1. Find the number of students who play neither sport:
- Number of students playing neither sport = Total number of male students - (number of students who play at least one sport)
= 200 - 90 = 110
2. Find the probability:
- Probability = (number of students who play neither sport) / (total number of male students)
= 110 / 200
= 0.55 or 55%
c) Probability of playing only basketball:
To find the probability that a randomly selected male student plays only basketball, we need to calculate the number of students who play only basketball divided by the total number of male students.
1. Find the number of students who play only basketball:
- Number of students who play only basketball = (number of students playing basketball) - (number of students playing both sports)
= 40 - 8 = 32
2. Find the probability:
- Probability = (number of students who play only basketball) / (total number of male students)
= 32 / 200
= 0.16 or 16%