Question

lauren has a bag that contains strawberry chews, lemon chews, and peach chews. she performs an experiment. lauren randomly removes a chew from the bag, records the result, and returns the chew to the bag. lauren performs the experiment 45 times. the results are shown below: a strawberry chew was selected 13 times. a lemon chew was selected 11 times. a peach chew was selected 21 times. based on these results, express the probability that the next chew lauren removes from the bag will be a flavor other than peach as a fraction in simplest form.

Explanation:

Step1: Calculate non - peach selections

The number of times a non - peach chew was selected is the sum of the number of strawberry and lemon chews. So, $13 + 11=24$.

Step2: Calculate probability

The probability $P$ of selecting a non - peach chew is the number of non - peach selections divided by the total number of experiments. The total number of experiments is 45. So, $P=\frac{24}{45}$.

Step3: Simplify the fraction

Find the greatest common divisor (GCD) of 24 and 45. The GCD of 24 and 45 is 3. Divide both the numerator and denominator by 3: $\frac{24\div3}{45\div3}=\frac{8}{15}$.

Answer:

$\frac{8}{15}$