Rolling a Fair Die: Probability of Getting At Least One Six After Multiple Rolls

In summary, the question asks how many times a fair die needs to be rolled to have a better than 50% chance of getting at least one six. The solution involves finding the probability of not getting a six with each roll and subtracting it from 1 until the probability drops below 50%.
  • #1
Amannequin
4
0
Homework Statement
How many times do we need to roll a fair die to get a better than evens chance of at least one six?

The attempt at a solution
Let n be the number of rolls. Am I trying to find how large n must be so P(At least one six)≥ 1/2?
I'm working on the basis that I need to solve the probability of the union of events Ai, where Ai denotes the event of rolling i sixes, i =1,2,3..., being greater than 1/2.
Any help or nudge in the right direction will be appreciated.
 
Physics news on Phys.org
  • #2
I'd attack it by finding the odds of NOT getting a six with one roll, then 2 rolls, then 3 rolls, and so on. As soon as that probability drops below 50% you've got the answer.
 
  • #3
Amannequin said:
Homework Statement
How many times do we need to roll a fair die to get a better than evens chance of at least one six?

The attempt at a solution
Let n be the number of rolls. Am I trying to find how large n must be so P(At least one six)≥ 1/2?
I'm working on the basis that I need to solve the probability of the union of events Ai, where Ai denotes the event of rolling i sixes, i =1,2,3..., being greater than 1/2.
Any help or nudge in the right direction will be appreciated.

P(at least one six) = 1 - P(no sixes)
 
  • #4
pasmith said:
P(at least one six) = 1 - P(no sixes)

Ah ... isn't that what I just said?
 

1. What is probability confusion?

Probability confusion refers to a common misunderstanding or misconception about how probability works. It often occurs when individuals misinterpret or misapply probability concepts, leading to incorrect conclusions or decisions.

2. How is probability confusion different from just not understanding probability?

Probability confusion is a type of misunderstanding specific to probability, while not understanding probability can refer to a general lack of knowledge or understanding about the subject. Probability confusion may occur even if someone has a basic understanding of probability, as it involves misapplying or misinterpreting concepts.

3. What are some common examples of probability confusion?

One common example of probability confusion is the gambler's fallacy, where individuals believe that past outcomes can influence future outcomes in a random process. Another example is the misunderstanding of the law of large numbers, where individuals expect a small sample size to accurately reflect the true probability of an event.

4. How can probability confusion be avoided?

To avoid probability confusion, it is important to have a solid understanding of basic probability concepts and to be aware of common misconceptions. It is also helpful to use tools such as visual aids or simulations to better understand probability in real-world scenarios.

5. How does probability confusion impact scientific research?

Probability confusion can greatly impact scientific research if it leads to incorrect conclusions or decisions. It is important for scientists to have a strong understanding of probability to accurately interpret data and make sound conclusions based on probability calculations.

Similar threads

Probability Generating Functions Question
    • Calculus and Beyond Homework Help
Replies
3
Views
1K
Chance of rolling at most one six with two dice in 20 rolls.
    • Calculus and Beyond Homework Help
Replies
2
Views
2K
Rolling Dice and Probability
    • Calculus and Beyond Homework Help
Replies
1
Views
2K
Probability: Dice Game between 20- and 12-sided dice with re-rolls
    • Precalculus Mathematics Homework Help
Replies
2
Views
1K
Probability of Rolling at Least One Six with Two Dice
    • Calculus and Beyond Homework Help
Replies
6
Views
2K
Probability of girls on a team getting shirts with pair numbers
    • Calculus and Beyond Homework Help
Replies
3
Views
737
Basic Probability Question—Rolling Die
    • Calculus and Beyond Homework Help
Replies
4
Views
7K
B Understanding Probability of Bias in Coin and Dice Tosses
    • Set Theory, Logic, Probability, Statistics
Replies
3
Views
1K
Probability of at Least One 6 in 5 out of 10 Rolls of Two Fair Dice
    • Calculus and Beyond Homework Help
Replies
11
Views
2K
Probability of Hall in H after John's Second Play: Markov Matrix Solution
    • Calculus and Beyond Homework Help
2
Replies
44
Views
3K

Hot Threads

Recent Insights

Back
Top