In box containing marbles 1-75, how many ways A) first marble are chosen

Answer, i think 1/75 Part B) two marbles are chosen i think answer are inconclusive Part C is ball with number 37 is chosen i think answer is 1/74

To find the answers to these questions, we need to understand the principles of probability and combinations.

Part A) Finding the number of ways to choose the first marble:
Since the box contains marbles numbered from 1 to 75, there are 75 equally likely choices for the first marble. Therefore, the answer is 75/75, which simplifies to 1.

Part B) Finding the number of ways to choose two marbles:
To calculate the number of ways to choose two marbles, we need to use combinations. The formula for combinations is given by: nCr = n! / ((n-r)! * r!).

In this case, we want to calculate 75C2, which represents choosing 2 marbles out of 75. Plugging the values into the formula, we get:
75C2 = 75! / ((75-2)! * 2!)

Simplifying the equation further:
75C2 = 75! / (73! * 2!)

Now, we can cancel out like terms:
75C2 = (75 * 74 * 73!) / (73! * 2!)

The 73! terms cancel out:
75C2 = 75 * 74 / 2

So, the answer is 75 * 74 / 2, which equals 2775.

Therefore, the answer to Part B is 2775 ways to choose two marbles from the box.

Part C) Finding the probability of choosing the ball numbered 37:
To find the probability, we need to know the total number of marbles and the number of marbles with the number 37. As given, there are 75 marbles in the box.

Since there is only one marble numbered 37, the probability of choosing it can be calculated as:
Probability = Number of favorable outcomes / Total number of possible outcomes

In this case, the number of favorable outcomes is 1 (choosing the ball numbered 37), and the total number of possible outcomes is 75 (the total number of marbles).

Therefore, the probability of choosing the ball with the number 37 is 1/75.