# Basic Probability: choosing without replacement

• lunds002
In summary, basic probability is the calculation of the likelihood that an event will occur when selecting objects or events from a given set. Choosing without replacement means that once an object or event is selected, it is not replaced before the next selection, affecting the probability of outcomes. This is calculated by dividing the number of desired outcomes by the total number of possible outcomes. When choosing with replacement, the selected object or event is put back into the set, while without replacement it is not, changing the total number of objects and affecting the probability of future selections. Understanding these concepts is crucial in scientific research as it allows for the calculation of probabilities and making informed decisions based on data.
lunds002

## Homework Statement

A box contains 22 red apples and 3 green apples. 3 apples are selected at random, one after the other, without replacement.

(a) The first two apples are green. What is the probability that the 3rd apple is red?

## The Attempt at a Solution

well if the first two are green, that means 2 of the 25 total apples are gone, so 23 remain. You have 22 red apples to choose from out of a total of 23.

Thus, I got P= 22/23

Correct?

That's correct.

## What is basic probability?

Basic probability is the measure of the likelihood that an event will occur. It involves understanding and calculating the chances of different outcomes when choosing objects or events from a given set.

## What does "choosing without replacement" mean in probability?

Choosing without replacement means that once an object or event is selected from a given set, it is not replaced or put back into the set before the next selection is made. This can affect the probability of certain outcomes.

## How is probability calculated when choosing without replacement?

The probability of an event occurring when choosing without replacement can be calculated by dividing the number of desired outcomes by the total number of possible outcomes. This changes with each selection, as the total number of objects in the set decreases.

## What is the difference between probability with replacement and without replacement?

When choosing with replacement, the selected object or event is put back into the set before the next selection is made. This means that the total number of objects in the set remains the same, and the probability of each selection is not affected by previous selections. When choosing without replacement, the selected object or event is not put back into the set, changing the total number of objects and affecting the probability of future selections.

## What is the importance of understanding basic probability and choosing without replacement in scientific research?

Understanding basic probability and choosing without replacement is crucial for scientists when conducting experiments or making predictions. It allows for the calculation of the likelihood of certain outcomes and helps in making informed decisions based on data and evidence. Additionally, it helps in minimizing bias and increasing the accuracy of results.

Replies
8
Views
2K
Replies
7
Views
1K
Replies
10
Views
1K
Replies
5
Views
2K
Replies
8
Views
463
Replies
25
Views
4K
Replies
3
Views
1K
Replies
10
Views
2K
Replies
24
Views
1K
Replies
3
Views
1K