Probability Dice Question

In summary, the conversation discusses the probability of at least two 6's appearing when a die is rolled 13 times. The initial solution provided was incorrect, and the group discusses using the complement to find the correct probability. They also discuss the difference between "at least two 6s appear" and "exactly two sixes appear." Ultimately, they come to the conclusion that using the complement is easier and more accurate.
  • #1
bap902
26
0

Homework Statement



A die is rolled 13 times. What is the probability of at least two 6's appearing? (Round your answer to four decimal places.)

2. The attempt at a solution
I know that the total number of outcomes is 6^13. I did (13nCr2)x(1x1x6x6x6x6x6x6x6x6x6x6x6)/6^13, but the answer isn't right. What am I doing wrong?
 
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  • #2
Perhaps you should try explaining the theory behind your solution.
I think working on the complement would be much easier. That is, finding the number of times a 6 would appear 0 times and the number of times a six would appear 1 time, and then take the complement.
 
  • #3
What is the difference between "at least two 6s appear" and "exactly two sixes appear?" which did you calculate?
VeeEight's suggestion is spot on.
 
  • #4
statdad said:
What is the difference between "at least two 6s appear" and "exactly two sixes appear?" which did you calculate?
VeeEight's suggestion is spot on.


I see. I calculated the number of times exactly two sixes would appear. Not quite sure how to do the compliment though.
 
  • #5
You can do separate cases (exactly two sixes, exactly three sixes, etc) and add them all up. It's just that taking the complement is less work
(a good exercise might be to do both to make sure they are the same)
 
  • #6
The complement of "at least two sixes" is "0 or 1 sixes" and is easier to calculate sinced it involves only two cases rather than 5.
 
  • #7
Thanks! Got it.
 

What is a "Probability Dice Question"?

A "Probability Dice Question" refers to a question that involves the use of dice to determine the likelihood of a particular outcome or event occurring.

How do you calculate the probability of rolling a specific number on a single die?

To calculate the probability of rolling a specific number on a single die, divide the number of desired outcomes (1) by the total number of possible outcomes (6), resulting in a probability of 1/6 or approximately 16.67%.

What is the difference between theoretical probability and experimental probability?

Theoretical probability is calculated based on the assumption that all outcomes are equally likely, while experimental probability is based on the actual results of an experiment or trial.

How do you calculate the probability of rolling a certain combination of numbers on multiple dice?

To calculate the probability of rolling a certain combination of numbers on multiple dice, multiply the individual probabilities of each number together. For example, the probability of rolling a 2 and a 4 on two six-sided dice would be (1/6) x (1/6) = 1/36 or approximately 2.78%.

Why is understanding probability important in science?

Understanding probability is important in science because it allows scientists to make predictions and draw conclusions based on data and experimental results. It also helps in determining the likelihood of certain events occurring and evaluating the reliability of experimental data.

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