Probability question (Counting)

In summary, probability is a measure of the likelihood of an event occurring and is expressed as a number between 0 and 1. Theoretical probability is based on mathematical calculations and assumes equal likelihood of all outcomes, while experimental probability is based on actual data. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Permutation involves arranging items in a specific order, while combination involves choosing items without considering the order. Probability is commonly used in real life, such as in finance, insurance, medicine, and games of chance.
  • #1
jtm
19
0
imagine a 8 letter word, how many possibilities are there to arrange letters in the alphabet (26) that start with BO(in that order) OR end with BO (in that order), if letters can be repeated?

This is my work:

1 * 1 * 26 * 26 * 26 * 26 * 26 * 26 = 26^6 +

26 * 26 * 26 * 26 * 26 * 26 * 1 * 1 = 26^6

BUT I'm not sure what the intersection is because:

do we subtract 1 or 26^4?

my logic from 26^4 is coming from BOLLLLBO <-- where L is any letter

Thank you!
 
Physics news on Phys.org
  • #2
Your logic sounds right.
 

Related to Probability question (Counting)

1. What is probability?

Probability is the measure of the likelihood that an event will occur. It is typically expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.

2. What is the difference between theoretical and experimental probability?

Theoretical probability is based on mathematical calculations and assumes that all outcomes are equally likely. Experimental probability is based on actual data collected from experiments or observations.

3. How do you calculate the probability of an event?

The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. This is known as the probability formula: P(event) = (number of favorable outcomes) / (total number of possible outcomes).

4. What is the difference between permutation and combination?

Permutation refers to the arrangement of items in a specific order, while combination refers to the selection of items without considering the order in which they are chosen. In other words, permutation involves rearranging a set of items, while combination involves selecting a subset of items.

5. How is probability used in real life?

Probability is used in a variety of fields, such as finance, insurance, and medicine, to make predictions and informed decisions. It is also commonly used in games of chance, such as gambling and lotteries.

Similar threads

  • Calculus and Beyond Homework Help
Replies
5
Views
817
  • Calculus and Beyond Homework Help
Replies
6
Views
2K
Replies
3
Views
1K
  • Calculus and Beyond Homework Help
Replies
7
Views
1K
  • Calculus and Beyond Homework Help
Replies
2
Views
2K
  • Set Theory, Logic, Probability, Statistics
Replies
5
Views
1K
  • Calculus and Beyond Homework Help
Replies
9
Views
11K
  • Calculus and Beyond Homework Help
Replies
3
Views
2K
  • Calculus and Beyond Homework Help
Replies
2
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
11
Views
1K
Back
Top