To find the probability that Martin's friend chooses a green grape and a seedless tangerine, we need to calculate the individual probabilities of each event and then multiply them together.

1. Probability of choosing a green grape:
   • Total number of grapes = 9 green grapes + 16 red grapes = 25 grapes.
   • Number of green grapes = 9.
   • Probability of choosing a green grape = \(\frac { 9} { 25} \).
2. Probability of choosing a seedless tangerine:
   • Total number of tangerines = 7 seeded tangerines + 3 seedless tangerines = 10 tangerines.
   • Number of seedless tangerines = 3.
   • Probability of choosing a seedless tangerine = \(\frac { 3} { 10} \).
3. Combined probability of both events happening:
   • The probability of choosing a green grape and a seedless tangerine = \(\frac { 9} { 25} \times \frac { 3} { 10} \).
     Now, let's calculate this:
     \[\frac { 9} { 25} \times \frac { 3} { 10} = \frac { 9 \times 3} { 25 \times 10} = \frac { 27} { 250} \]

Supplemental Knowledge

• Probability is the measure of the likelihood that an event will occur. It ranges from 0 (impossible event) to 1 (certain event). When dealing with compound events, where two or more events are combined, the probability of both events occurring is found by multiplying the probability of each individual event.
  For example, if you have a bag with 5 red balls and 3 blue balls, and you want to find the probability of drawing a red ball followed by a blue ball without replacement, you would calculate:

• Probability of drawing a red ball: \(\frac { 5} { 8} \)
• After drawing one red ball, there are now 7 balls left.
• Probability of then drawing a blue ball: \(\frac { 3} { 7} \)
  The combined probability is:
  \[\frac { 5} { 8} \times \frac { 3} { 7} = \frac { 15} { 56} \]

Knowledge in Action

Understanding compound probability can be very useful in everyday decision-making. For instance, if you're planning an outdoor event and want to know the likelihood of having good weather on both Saturday and Sunday, you would use compound probability. If there's a 70% chance of good weather each day independently, then the chance of having good weather on both days is:
\[0.7 \times 0.7 = 0.49\]
So there's a 49% chance that both days will have good weather.

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