Of 162 students honored at an academic awards banquet, 48 won awards for mathematics and 78 won awards for English. There are 14 students who won awards for both mathematics and English. A student is selected at random for an interview. What is the probability that the student won an award for English or mathematics? Express your first answer as a fraction in simplest form. Round your percent answer to the nearest tenth. The probability that the student interviewed won an award for English or mathematics is , or about $\%$% .
Question
Of 162 students honored at an academic awards banquet, 48 won awards for mathematics and 78 won awards for English. There are 14 students who won awards for both mathematics and English. A student is selected at random for an interview. What is the probability that the student won an award for English or mathematics? Express your first answer as a fraction in simplest form. Round your percent answer to the nearest tenth. The probability that the student interviewed won an award for English or mathematics is , or about % .
Solution
To solve this problem, we first need to find the total number of students who won awards for either Mathematics or English.
We know that 48 students won awards for Mathematics and 78 won awards for English. However, we also know that 14 students won awards for both subjects. So, if we simply add the number of Math and English awards together, we would be counting these 14 students twice.
To avoid this, we subtract the 14 students who won both awards from our total.
So, the total number of students who won an award in either subject is 48 (Math awards) + 78 (English awards) - 14 (double counted) = 112 students.
The probability of an event is calculated by dividing the number of ways the event can occur by the total number of outcomes. In this case, the event is a student winning an award in either Math or English, and the total number of outcomes is the total number of students, which is 162.
So, the probability is 112 (students who won in either subject) / 162 (total students) = 0.691358024691358 (when not rounded).
To express this as a fraction, we can say that the probability is 112/162.
To express this as a percentage, we multiply the probability by 100, which gives us 69.1358024691358%.
Rounding to the nearest tenth, we get 69.1%.
So, the probability that the student interviewed won an award for English or Mathematics is 112/162, or about 69.1%.
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