UpStudy Free Solution:

To find the probability that Martin's friend chooses a green grape and a seedless tangerine, we need to follow these steps:

1. Calculate the probability of choosing a green grape:

- Total number of grapes = 9 green grapes + 16 red grapes = 25 grapes.

- Probability of choosing a green grape = \(\frac { 9} { 25} \).

2. Calculate the probability of choosing a seedless tangerine:

- Total number of tangerines = 7 seeded tangerines + 3 seedless tangerines = 10 tangerines.

- Probability of choosing a seedless tangerine = \(\frac { 3} { 10} \).

3. Calculate the combined probability of both events happening:

- Since the choice of grape and tangerine are independent events, we multiply the probabilities:

\[\text { Probability of green grape and seedless tangerine} = \left ( \frac { 9} { 25} \right ) \times \left ( \frac { 3} { 10} \right ) = \frac { 9 \times 3} { 25 \times 10} = \frac { 27} { 250} .\]

Therefore, the probability that Martin's friend chooses a green grape and a seedless tangerine is:

\[\frac { 27} { 250} \]

Supplemental Knowledge

In probability, the likelihood of a compound event occurring is determined by multiplying the probabilities of each individual event. For independent events \(A\) and \(B\), the probability of both events occurring is given by:

\[P( A \text { and } B) = P( A) \times P( B) \]

To solve this problem, we need to calculate:

1. The probability of choosing a green grape from the bowl of grapes.

2. The probability of choosing a seedless tangerine from the bowl of tangerines.

Then, we multiply these probabilities to find the overall probability.

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