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?

Question

Sam Dunlap

Mathematics

25 December, 19:40

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?

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Answers (1)

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Braiden Phillips · Answer 1

There are 10 juice boxes in the cooler altogether.

2 of them are grape.

The first time Jill pulls one out with her eyes closed,

the probability that it's a grape is

2 / 10.

If that try is successful, then there are 9 boxes left in the cooler,

and one of them is grape.

If she already has one grape, and reaches in again with her eyes

closed, the probability of pulling out the second grape is

1 / 9.

The probability of both events happening in two tries is

(2/10) x (1/9) = 2/90 = 1/45 = (2 and 2/9) percent.