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In a particular school assembly of $120$ students, there are $40$ first graders, $20$ of which are girls. If one student is chosen at random, what is the probability that the chosen student vill not be a first grade girl?

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Probability of independent and dependent events

Full solution

Q. In a particular school assembly of

120

students, there are

40

first graders,

20

of which are girls. If one student is chosen at random, what is the probability that the chosen student vill not be a first grade girl?

Determine Total First Grade Girls: First, we need to determine the total number of first grade girls in the assembly. $\newline$ There are $40$ first graders and half of them are girls, so there are $20$ first grade girls.
Calculate Students Not First Grade Girls: Next, we calculate the number of students who are not first grade girls. Since there are $120$ students in total and $20$ of them are first grade girls, the number of students who are not first grade girls is $120 - 20 = 100$ .
Find Probability: Now, we find the probability that the chosen student will not be a first grade girl. $\newline$ The probability is the number of students who are not first grade girls divided by the total number of students. $\newline$ So, the probability is $\frac{100}{120}$ .
Simplify Fraction: We can simplify the fraction $\frac{100}{120}$ by dividing both the numerator and the denominator by their greatest common divisor, which is $20$ . $\newline$ $100 \div 20 = 5$ and $120 \div 20 = 6$ . $\newline$ So, the simplified fraction is $\frac{5}{6}$ .

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