Question

A bowl has 8 green grapes and 15 red grapes. Henry randomly chooses a grape, eats it, and then chooses another grape. What is the probability that both grapes are red?

Answer 1

In this item there are a total of 23 grapes. The number of sample space for this item is equal to permutation of 23 taken 2 because the order is of importance in this item,
23P2 = 506

Then, the way that red grapes can be taken is equal to,
8 x 7
which is simplified into 56. The probability calculation is then shown below,
P = (56/506) x 100% = 11.067%

Answer: 11%

Answer 2

Probability is defined as the likelihood of an event occurring based on chance. In this case it involves choosing without replacement such that any time a grape is chosen the color of the chosen decreases and so does the total grapes.
The total number of grapes is 23 and the red grapes are 15, therefore the probability of choosing a red grape the first time is 15/23, and the probability of choosing the red grape the second time will be 14/22 ( because the number of red grapes has already decreased by one and so is the total number of grapes after first choice). Hence, the probability of choosing or eating two red grapes will be 15/23×14/22 =105/253 or 0.415