Eighteen marbles are dropped into a jar. There are 8 black marbles, 7 red ones, and 3 silver ones. Marbles are taken from the jar without looking. Use this information to answer these two questions.

1. If one marble is taken, what is the probability of taking a marble that is NOT black?

2. If two marbles are taken WITHOUT replacement, what is the probability of choosing a black marble first and a silver marble second?

1. 10/18

2. Black first = 8/18, without replacement, silver is 3/17. To find probability of all events occurring, multiply probability of individual events.

8/18

To answer both questions, we need to first determine the total number of marbles in the jar and then the number of marbles that satisfy the conditions for each question.

1. Probability of taking a marble that is NOT black:
To calculate the probability of selecting a non-black marble, we need to determine the number of marbles that are not black and divide it by the total number of marbles.

Total Number of Marbles: 18
Number of Black Marbles: 8
Number of Non-Black Marbles: Total Number of Marbles - Number of Black Marbles = 18 - 8 = 10

The probability of selecting a non-black marble is given by:
Probability = Number of Non-Black Marbles / Total Number of Marbles = 10 / 18 = 5/9 or approximately 0.5556

Therefore, the probability of taking a marble that is not black is 5/9 or approximately 0.5556.

2. Probability of choosing a black marble first and a silver marble second:
If two marbles are taken without replacement, the probability of selecting a black marble first and a silver marble second involves considering the number of black marbles and the number of silver marbles in the jar.

Total Number of Marbles: 18
Number of Black Marbles: 8
Number of Silver Marbles: 3

To calculate the probability, we first find the probability of selecting a black marble first:
Probability of Selecting a Black Marble First = Number of Black Marbles / Total Number of Marbles = 8 / 18 = 4/9 or approximately 0.4444

Now, since we have not replaced the first marble, the denominator becomes 17 (total marbles - 1). The number of the second event (selecting a silver marble) decreases by 1:
Number of Silver Marbles (after one black marble is selected): 3 - 1 = 2

The probability of selecting a silver marble second, after taking a black marble first, is:
Probability of Selecting a Silver Marble Second = Number of Silver Marbles / Total Number of Marbles (after one black marble is selected) = 2 / 17

To calculate the probability of both events occurring, we multiply the individual probabilities:
Probability of selecting a black marble first and a silver marble second = Probability of Selecting a Black Marble First × Probability of Selecting a Silver Marble Second
= (4/9) × (2/17) = 8/153 or approximately 0.05229

Therefore, the probability of choosing a black marble first and a silver marble second is 8/153 or approximately 0.05229.