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In a class of students, the following data table summarizes how many students have a brother or a sister. What is the probability that a student chosen randomly from the class has a sister? & }(c) Has a brother & Does not have a brother Has a sister & 8 & 4 Does not have a sister & 2 & 6

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In a class of students, the following data table summarizes how many students have a brother or a sister. What is the probability that a student chosen randomly from the class has a sister?

 & }(c)
Has a 
brother
 & 
Does not have a 
brother
 
 Has a sister & 8 & 4 
 
Does not have a 
sister
 & 2 & 6

In a class of students, the following data table summarizes how many students have a brother or a sister. What is the probability that a student chosen randomly from the class has a sister? & }(c) Has a brother & Does not have a brother Has a sister & 8 & 4 Does not have a sister & 2 & 6

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BridgetExpert · Tutor for 3 years

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To find the probability that a student chosen randomly from the class has a sister, we need to look at the total number of students who have a sister and divide that by the total number of students in the class.Step 1: Identify the number of students who have a sister.From the table, we can see that there are 8 students who have both a brother and a sister, and there are 4 students who have a sister but do not have a brother. So, the total number of students who have a sister is \(8 + 4 = 12\).Step 2: Calculate the total number of students in the class.To find the total number of students, we add up all the numbers in the table:\(8\) (students with a brother and a sister) \(+\)\(4\) (students with a sister but no brother) \(+\)\(2\) (students with a brother but no sister) \(+\)\(6\) (students with neither a brother nor a sister) \(=\)\(8 + 4 + 2 + 6 = 20\) students in total.Step 3: Calculate the probability.The probability \(P\) that a randomly chosen student has a sister is the number of students with a sister divided by the total number of students:\[P(\text{has a sister}) = \frac{\text{Number of students with a sister}}{\text{Total number of students}} = \frac{12}{20}\]Step 4: Simplify the fraction.The fraction \(\frac{12}{20}\) can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 4:\[\frac{12 \div 4}{20 \div 4} = \frac{3}{5}\]Step 5: Provide the final answer.The probability that a randomly chosen student from the class has a sister is \(\boxed{\frac{3}{5}}\).
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