Question

There are 797 identical plastic chips numbered 1 through 797 in a box. What is the probability of reaching into the box and randomly drawing a chip number that is smaller than 507

Answer 1

The probability of drawing a chip numbered less than 507 from a box of 797 chips is calculated by dividing the favorable outcomes (chips numbered 1 through 506) by the total number of possible outcomes (chips numbered 1 through 797), resulting in a probability of 506/797.

Step-by-step explanation:

The student's question pertains to the calculation of a probability associated with a random draw of a plastic chip from a box containing chips numbered from 1 to 797. The specific task is to find the probability of drawing a chip with a number less than 507.

To calculate this probability, we need to identify the total number of favorable outcomes and the total number of possible outcomes. The number of favorable outcomes is the count of all chips numbered less than 507, which are the numbers 1 through 506. There are exactly 506 favorable outcomes in this scenario. The total number of possible outcomes is simply the total number of chips, which is 797.

The probability is then calculated by dividing the number of favorable outcomes by the total number of possible outcomes, which is:

Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes
Probability = 506 / 797

Therefore, the probability of randomly drawing a chip numbered less than 507 is 506/797.

Answer 2

0.6357 = 63.57% probability of reaching into the box and randomly drawing a chip number that is smaller than 507

Step-by-step explanation:

The probability of drawing each chip is the same, which means that the uniform distribution is used to solve this question.

Uniform distribution:

A distribution is called uniform if each outcome has the same probability of happening.

The uniform distribution has two bounds, a and b, and the probability of finding a value lower than x is given by:

`P(X < x) = (x - a)/(b - a)`

There are 797 identical plastic chips numbered 1 through 797 in a box.

This means that
`a = 1, b = 797`

What is the probability of reaching into the box and randomly drawing a chip number that is smaller than 507?

`P(X < 507) = (507 - 1)/(797 - 1) = 0.6357`

0.6357 = 63.57% probability of reaching into the box and randomly drawing a chip number that is smaller than 507