there were 3 apple, 1 mixed fruit, 2 grape, and 4 tropical fruit juice boxes in the cooler at the picnic…

there were 3 apple, 1 mixed fruit, 2 grape, and 4 tropical fruit juice boxes in the cooler at the picnic. what is the probability that, when jill reaches into the cooler to grab two juice boxes without replacing them, she grabs two that are grape?\n$\frac{1}{100}$\n$\frac{1}{50}$\n$\frac{1}{45}$\n$\frac{1}{25}$

there were 3 apple, 1 mixed fruit, 2 grape, and 4 tropical fruit juice boxes in the cooler at the picnic. what is the probability that, when jill reaches into the cooler to grab two juice boxes without replacing them, she grabs two that are grape?\n$\frac{1}{100}$\n$\frac{1}{50}$\n$\frac{1}{45}$\n$\frac{1}{25}$

Answer

Explanation:

Step1: Calculate total number of juice boxes

$3 + 1+2 + 4=10$

Step2: Calculate probability of first - grape juice box

The probability of grabbing a grape juice box on the first pick is $\frac{2}{10}$ since there are 2 grape juice boxes out of 10 total.

Step3: Calculate probability of second - grape juice box

After one grape juice box is picked, there is 1 grape juice box left and 9 total juice boxes left. So the probability of grabbing a grape juice box on the second pick is $\frac{1}{9}$.

Step4: Calculate probability of both events

Since these are dependent events, we multiply the probabilities of each event. So the probability of grabbing two grape juice boxes is $\frac{2}{10}\times\frac{1}{9}=\frac{2}{90}=\frac{1}{45}$

Answer:

$\frac{1}{45}$