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

First, find the total number of juice boxes. Add the number of each type: \( 3 + 1 + 2 + 4 = 10 \) juice boxes.

Step2: Probability of first grape

The number of grape juice boxes is 2. The probability of picking a grape juice box first is \( \frac{2}{10} \).

Step3: Probability of second grape (without replacement)

After picking one grape juice box, there is 1 grape juice box left and 9 total juice boxes left. So the probability of picking a grape juice box second is \( \frac{1}{9} \).

Step4: Multiply the probabilities

To find the probability of both events happening (picking two grape juice boxes), multiply the two probabilities: \( \frac{2}{10} \times \frac{1}{9} = \frac{2}{90} = \frac{1}{45} \).

Answer:

\(\frac{1}{45}\) (corresponding to the option \(\boldsymbol{\frac{1}{45}}\))