Pregunta
Question 6 ( 2 marks)
In a group of 50 people there are 30 who are on the on the athletics team and 27 who play
basketball. Twelve of the people on the athletics team also play basketball and five people in the
class are involved in neither.
A person from the group is chosen at random.
(a) What is the probability that the person is on the athletics team and plays basketball?
b) What is the probability that the person is on the athletics team or plays basketball, or
both?
In a group of 50 people there are 30 who are on the on the athletics team and 27 who play
basketball. Twelve of the people on the athletics team also play basketball and five people in the
class are involved in neither.
A person from the group is chosen at random.
(a) What is the probability that the person is on the athletics team and plays basketball?
b) What is the probability that the person is on the athletics team or plays basketball, or
both?
Ask by Simmons Allan. in Australia
Jan 23,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
(a) The probability that the person is on the athletics team and plays basketball is 0.24.
(b) The probability that the person is on the athletics team or plays basketball, or both is 0.9.
Solución
To solve this problem, we will use the principles of set theory and probability.
Known Conditions:
- Total number of people in the group,
- Number of people on the athletics team,
- Number of people who play basketball,
- Number of people on both teams,
- Number of people involved in neither,
Step-by-Step Solution:
(a) Probability that the person is on the athletics team and plays basketball
The probability
can be calculated using the formula:
Where:
-
(people on both teams) -
(total people)
Now, substituting the values:
Calculating this gives:
(b) Probability that the person is on the athletics team or plays basketball, or both
To find the probability
, we can use the formula:
Where:
-
-
-
(calculated in part a)
Now substituting these values into the formula:
Calculating this gives:
Final Answers:
(a) The probability that the person is on the athletics team and plays basketball is
.
(b) The probability that the person is on the athletics team or plays basketball, or both is
.
Respondido por UpStudy AI y revisado por un tutor profesional
Como
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Mind Expander
To tackle the questions, let’s break it down with some fun facts!
The number of people who are on both teams is a classic example of set overlap! Here, we can easily identify the groups. Since there are 30 in athletics and 27 basketball players, we know that 12 are in both groups. So, the total unique participants in at least one sport can be found using the principle of inclusion-exclusion!
Now to put the formulas into action:
(a) The probability of selecting someone who is on both teams is simply the number of people in both groups (12) divided by the total number of people (50), so it’s 12/50 or 0.24!
(b) To find the probability of being on either team (or both), we count the unique athletes: 30 (athletics) + 27 (basketball) - 12 (both) = 45. Thus, the probability is 45/50 or 0.90! Pretty neat, right?
(a) The probability of selecting someone who is on both teams is simply the number of people in both groups (12) divided by the total number of people (50), so it’s 12/50 or 0.24!
(b) To find the probability of being on either team (or both), we count the unique athletes: 30 (athletics) + 27 (basketball) - 12 (both) = 45. Thus, the probability is 45/50 or 0.90! Pretty neat, right?
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