lauren has a bag that contains strawberry chews, lemon chews, and peach chews. she performs an experiment…

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.

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.

Answer

Explanation:

Step1: Calculate non - peach selections

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

Step2: Calculate the probability

The probability $P$ of an event is the number of favorable outcomes divided by the total number of outcomes. The total number of experiments is 45. So the probability that the next chew is not peach is $\frac{24}{45}$.

Step3: Simplify the fraction

To simplify $\frac{24}{45}$, 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:

$\frac{8}{15}$