Question

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?
\\(\frac{1}{100}\\)
\\(\frac{1}{50}\\)
\\(\frac{1}{45}\\)
\\(\frac{1}{25}\\)

Explanation:

Step1: Calculate total juice boxes

$3 + 1+2 + 4=10$

Step2: Calculate probability of first - grape box

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

Step3: Calculate probability of second - grape box

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

Step4: Calculate combined probability

The probability of both events happening (grabbing two grape boxes) is the product of the probabilities of each event. So $P=\frac{2}{10}\times\frac{1}{9}=\frac{2}{90}=\frac{1}{45}$

Answer:

$\frac{1}{45}$