Martin puts two bowls of fruit out for his friends. The bowl of grapes has 9 green grapes and 16 red grapes. The bowl of tangerines has 7 seeded and 3 seedless tangerines. Martin’s friend chooses a random grape and a random tangerine. What is the probability that she chooses a green grape and a seedless tangerine?
The correct answer and explanation is:
To find the probability that Martin’s friend chooses a green grape and a seedless tangerine, we can use the multiplication rule for independent events, since choosing a grape and choosing a tangerine are separate, independent events.
Step 1: Total number of grapes
There are:
- 9 green grapes
- 16 red grapes
Total grapes = 9 + 16 = 25
So, the probability of choosing a green grape is: P(green grape)=925P(\text{green grape}) = \frac{9}{25}
Step 2: Total number of tangerines
There are:
- 7 seeded tangerines
- 3 seedless tangerines
Total tangerines = 7 + 3 = 10
So, the probability of choosing a seedless tangerine is: P(seedless tangerine)=310P(\text{seedless tangerine}) = \frac{3}{10}
Step 3: Multiply the two probabilities
Since both selections are independent, multiply the probabilities: P(green grape and seedless tangerine)=925×310=27250P(\text{green grape and seedless tangerine}) = \frac{9}{25} \times \frac{3}{10} = \frac{27}{250}
✅ Final Answer: 27250\frac{27}{250}
📘 Explanation (Approx. 300 words)
To solve this probability problem, it’s important to recognize that two separate events are occurring: one fruit is selected from the bowl of grapes, and one from the bowl of tangerines. Since these actions don’t affect each other (the selection of a grape doesn’t impact the selection of a tangerine), we treat them as independent events. This means we can find the overall probability by multiplying the probabilities of each individual event.
First, we calculate the probability of selecting a green grape. The grape bowl contains 9 green grapes out of a total of 25 (9 green + 16 red). Therefore, the chance of picking a green grape is 9 out of 25, or 925\frac{9}{25}.
Next, we find the probability of selecting a seedless tangerine. There are 3 seedless tangerines in a total of 10 (7 seeded + 3 seedless), so the probability of picking a seedless tangerine is 310\frac{3}{10}.
To find the probability of both events happening together—selecting a green grape and a seedless tangerine—we multiply the two individual probabilities: 925×310=27250\frac{9}{25} \times \frac{3}{10} = \frac{27}{250}
This product represents the likelihood that both specific types of fruit are chosen at random. Fraction multiplication is straightforward: multiply the numerators (top numbers) together and multiply the denominators (bottom numbers) together. This gives us the final answer: 27250\frac{27}{250}, which cannot be simplified further.