7/170
This problem asks for the probability of two independent events occurring together. An independent event is one where the outcome is not affected by the outcomes of other events. In this case, selecting a candy from the first bag has no impact on the selection from the second bag, so we can calculate the probability of each event separately and then multiply them to find the combined probability.
First, let’s determine the probability of selecting a strawberry candy from the first bag. The problem states that Julio pulled 8 pineapple, 5 lime, and 7 strawberry candies. To find the total number of observed outcomes, we add these pulls together: 8 + 5 + 7 = 20 total pulls from the first bag. The number of favorable outcomes, which is pulling a strawberry candy, is 7. Therefore, the experimental probability of pulling a strawberry candy from the first bag is the number of strawberry pulls divided by the total number of pulls, which gives us a probability of 7/20.
Next, we calculate the probability of selecting a tamarind candy from the second bag. Julio pulled 9 mango, 2 tamarind, and 6 watermelon candies from this bag. The total number of pulls from the second bag is the sum of these individual pulls: 9 + 2 + 6 = 17 total pulls. The number of favorable outcomes for this event, pulling a tamarind candy, is 2. So, the probability of pulling a tamarind candy from the second bag is 2/17.
To find the probability that both events will happen during the next selection, we multiply the individual probabilities. The probability of getting a strawberry from the first bag AND a tamarind from the second bag is calculated as (7/20) × (2/17). When multiplying fractions, we multiply the numerators together and the denominators together. This gives us (7 × 2) / (20 × 17) = 14/340.
Finally, we should simplify the resulting fraction to its lowest terms. Both the numerator (14) and the denominator (340) are even numbers, so they can be divided by 2. Dividing 14 by 2 gives 7, and dividing 340 by 2 gives 170. This results in the simplified fraction 7/170. Since 7 is a prime number and 170 is not divisible by 7, the fraction cannot be simplified further.
