Finding the Probability of Picking a Family Member's Name: A Case of Two Tries

  • Thread starter Thread starter Reward
  • Start date Start date
  • Tags Tags
    Probability
Click For Summary
SUMMARY

The probability of a family of five members picking names without selecting their own name is calculated using combinatorial methods. The specific scenario discussed involves determining the probability that it takes exactly two tries for all members to successfully pick a name that is not their own. The solution involves understanding derangements and the application of the formula for permutations, leading to a definitive probability outcome for this two-try scenario.

PREREQUISITES
  • Understanding of basic probability theory
  • Familiarity with combinatorial mathematics
  • Knowledge of derangements in permutations
  • Ability to apply mathematical formulas for probability calculations
NEXT STEPS
  • Study the concept of derangements in detail
  • Learn about permutations and combinations in probability
  • Explore advanced probability scenarios involving multiple trials
  • Investigate real-world applications of probability theory in decision-making
USEFUL FOR

Mathematicians, educators, students studying probability, and anyone interested in combinatorial problems and their applications in real-life scenarios.

Reward
Messages
1
Reaction score
0
A family of five people randomly picks a name of a family member from a hat to decide for whom to buy a present.
What is the probability that nobody picks their own name?
If someone picks their own name, all the names are returned and everyone picks again. What is the probability that it took exactly two tries for everyone to pick a name of another family member:confused:
 
Physics news on Phys.org

Similar threads

MHB Find Probability of two polygons
  • · Replies 21 ·
Replies
21
Views
5K
High School The Probability of an Event
  • · Replies 11 ·
Replies
11
Views
2K
Graduate Probability of finding a k-subset in a d-dimensional random
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Making Sense of Notation Confusion in Statistical Digital Signal Processing
  • · Replies 6 ·
Replies
6
Views
2K
Solving Probability Problem: Find P(Exactly 1 Person Gets Own Name Tag)
  • · Replies 5 ·
Replies
5
Views
3K
MHB Calculating Probabilities in Poker Hand: An Example
  • · Replies 1 ·
Replies
1
Views
2K
What is the probability of guessing 3 digits out of an 8-digit number?
  • · Replies 5 ·
Replies
5
Views
3K
High School Conditional Probability, Independence, and Dependence
  • · Replies 10 ·
Replies
10
Views
3K
Weird 'Services for this domain name disabled' error on another site
  • · Replies 17 ·
Replies
17
Views
2K
Probability/Combinatorics: # ways of picking 5 from 3 groups of 6
  • · Replies 7 ·
Replies
7
Views
2K