Jacob has a bag of his favorite marbles. It has 3 red marbles, 4 blue, and 10 of his most favorite color, neon orange. What is the probability that, if he removes 2 marbles without looking and without replacement, he will get two orange marbles

The probability that, if he removes 2 marbles without looking and without replacement, he will get two orange marbles is 0.3309.

Given that,

Jacob has a bag of his favorite marbles.

It has 3 red marbles, 4 blue, and 10 of his most favorite color, neon orange.

We have to find,

What is the probability that, if he removes 2 marbles without looking and without replacement, he will get two orange marbles.

According to the question,

It has 3 red marbles, 4 blue, and 10 of his most favorite color, neon orange.

Total number of marbles = 3 + 4 + 10 = 17

The probability that the first selection of orange is,

The selection without replacement, the number of orange marbles and the total number of marbles would decrease by 1, respectively.

Therefore,

The required probability is,

The probability that the selection is orange is 0.3309.

Hence, The probability that, if he removes 2 marbles without looking and without replacement, he will get two orange marbles is 0.3309.

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Step-by-step explanation:

Given

Required

Probability of selecting 2 orange marbles

The total number of marbles is:

The probability that the first selection is orange is:

Because it is a selection without replacement, the number of orange marbles and the total number of marbles would decrease by 1, respectively.

So, the probability that the selection is orange is:

The required probability is: