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 probability of choosing a green grape

The bowl of grapes has 9 green grapes and 16 - 9=7 red grapes. The probability of choosing a green grape from the bowl of grapes is $P(\text{green grape})=\frac{9}{16}$.

Step2: Calculate probability of choosing a seedless tangerine

The bowl of tangerines has 3 seedless and 7 seeded tangerines. The probability of choosing a seedless tangerine from the bowl of tangerines is $P(\text{seedless tangerine})=\frac{3}{7 + 3}=\frac{3}{10}$.

Step3: Calculate the joint - probability

Since the events of choosing a grape and a tangerine are independent, the probability of choosing a green grape and a seedless tangerine is the product of their individual probabilities. So $P = \frac{9}{16}\times\frac{3}{10}=\frac{27}{160}$.

Answer:

$\frac{27}{160}$