Question: A box contains 40 pens of equal size. 10 of them are green and 18 are red. If a pen is chosen at…

A box contains 40 pens of equal size. 10 of them are green and 18 are red. If a pen is chosen at random from the box, what is the probability that it is neither green nor red?

Solution

To find the probability that a pen chosen at random is neither green nor red, we first need to determine how many pens are neither green nor red. First, calculate the total number of pens that are either green or red: \[ 10 + 18 = 28 \] Next, find the number of pens that are neither green nor red by subtracting the number of green and red pens from the total number of pens: \[ 40 - 28 = 12 \] Now, calculate the probability that a pen is neither green nor red by dividing the number of pens that are neither green nor red by the total number of pens: \[ \frac{12}{40} = \frac{3}{10} \] So, the probability that a pen chosen at random is neither green nor red is \(\frac{3}{10}\).