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In a class of students, the following data table summarizes how many students play an instrument or a sport. What is the probability that a student chosen randomly from the cla plays a sport or an instrument? & }(c) Plays an instrument & Does not play an instrument Plays a sport & 6 & 4 Does not play a sport & 5 & 3

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In a class of students, the following data table summarizes how many students play an instrument or a sport. What is the probability that a student chosen randomly from the cla plays a sport or an instrument?

 & }(c)
Plays an 
instrument
 & 
Does not play an 
instrument
 
 Plays a sport & 6 & 4 
 
Does not play a 
sport
 & 5 & 3

In a class of students, the following data table summarizes how many students play an instrument or a sport. What is the probability that a student chosen randomly from the cla plays a sport or an instrument? & }(c) Plays an instrument & Does not play an instrument Plays a sport & 6 & 4 Does not play a sport & 5 & 3

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MaisyProfessional · Tutor for 6 years

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To find the probability that a student chosen randomly from the class plays a sport or an instrument, we need to consider all the students who play either one or both of these activities.Step 1: Define the events.Let $A$ be the event "the student plays a sport" and $B$ be the event "the student plays an instrument".Step 2: Identify the sample space and the event.The sample space consists of all the students in the class. The event we are interested in is $A \cup B$, which means "the student plays a sport or an instrument".Step 3: Count the number of outcomes in the event $A \cup B$.To find the number of students who play a sport or an instrument, we add the number of students who play a sport, the number of students who play an instrument, and subtract the number of students who play both (to avoid double-counting).From the table:- The number of students who play a sport is $6 + 4 = 10$.- The number of students who play an instrument is $6 + 5 = 11$.- The number of students who play both a sport and an instrument is $6$.Therefore, the number of students who play a sport or an instrument is $10 + 11 - 6 = 15$.Step 4: Find the total number of outcomes.To find the total number of students, we add all the numbers in the table.\[6 + 4 + 5 + 3 = 18\]Step 5: Calculate $P(A \cup B)$.The probability of event $A \cup B$ is the number of outcomes in event $A \cup B$ divided by the total number of outcomes.\[P(A \cup B) = \frac{\# \text{ of outcomes in } A \cup B}{\text{total } \# \text{ of outcomes}}\]\[P(A \cup B) = \frac{15}{18}\]Step 6: Simplify the fraction.\[P(A \cup B) = \frac{15}{18} = \frac{5}{6}\]The probability that a student chosen randomly from the class plays a sport or an instrument is $\boxed{\frac{5}{6}}$.
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