Question

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. martins friend chooses a random grape and a random tangerine. what is the probability that she chooses a green grape and a seedless tangerine? enter the answer in the box.

Explanation:

Step1: Calculate total grapes

Total grapes = green grapes + red grapes = \( 9 + 16 = 25 \)

Step2: Probability of green grape

Probability of green grape \( P(G) = \frac{\text{green grapes}}{\text{total grapes}} = \frac{9}{25} \)

Step3: Calculate total tangerines

Total tangerines = seeded + seedless = \( 7 + 3 = 10 \)

Step4: Probability of seedless tangerine

Probability of seedless tangerine \( P(S) = \frac{\text{seedless tangerines}}{\text{total tangerines}} = \frac{3}{10} \)

Step5: Probability of both events

Since the events are independent, multiply the probabilities: \( P(G \cap S) = P(G) \times P(S) = \frac{9}{25} \times \frac{3}{10} = \frac{27}{250} \)

Answer:

\(\frac{27}{250}\)