Question

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

Answer 1

Answer:

$P(1\ and\ 2) = 0.3309$

Step-by-step explanation:

Given

$Red = 3$

$Blue = 4$

$Orange=10$

Required

Probability of selecting 2 orange marbles

The total number of marbles is:

$Total = Red + Blue + Orange$

$Total = 3 + 4 + 10$

$Total = 17$

The probability that the first selection is orange is:

$P(1) = \frac{10}{17}$

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:

$P(2) = \frac{10-1}{17-1}$

$P(2) = \frac{9}{16}$

The required probability is:

$P(1\ and\ 2) = P(1) * P(2)$

$P(1\ and\ 2) = \frac{10}{17} * \frac{9}{16}$

$P(1\ and\ 2) = \frac{10*9}{17*16}$

$P(1\ and\ 2) = \frac{90}{272}$

$P(1\ and\ 2) = 0.3309$

Answer 2

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,

$P(1) = \dfrac{10}{17}$

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

$P(2) = \dfrac{10-1}{17-1}\\\\P(2) = \dfrac{9}{16}$

Therefore,

The required probability is,

$P(1 \ and\ 2) = P(1) \times P(2)\\\\P(1 \ and \ 2)= \dfrac{10}{17} \times \dfrac{9}{16}\\\\P(1 \ and \ 2) = \dfrac{90}{272}\\\\P(1 \ and \ 2) = 0.3309$

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.

To know more about the Probability click the link given below.

https://brainly.com/question/20638895