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:

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

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

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

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

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