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.
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.
Solution
The probability of an event is calculated by dividing the number of successful outcomes by the total number of outcomes. In this case, the successful outcome is selecting a chew that is not peach, and the total number of outcomes is the total number of chews.
From the experiment, we know that a strawberry chew was selected 13 times, a lemon chew was selected 11 times, and a peach chew was selected 21 times. This gives us a total of 45 chews.
The number of successful outcomes (selecting a chew that is not peach) is the number of times a strawberry chew was selected plus the number of times a lemon chew was selected. This is 13 + 11 = 24.
So, the probability that the next chew Lauren removes from the bag will be a flavor other than peach is 24/45.
To simplify this fraction, we find the greatest common divisor (GCD) of 24 and 45, which is 3. Dividing both the numerator and the denominator by 3, we get 8/15.
So, the probability that the next chew Lauren removes from the bag will be a flavor other than peach is 8/15 in simplest form.
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