What is the probability of throwing the same number exactly 3 times?

In summary, the conversation discusses the probability of throwing the same number exactly 3 times when throwing a dice 5 times. The first attempt calculated this probability to be 0.0192901, but did not take into account all possible options. The second attempt used the binomial distribution method to calculate the probability, resulting in 0.03215. However, this method also did not consider all possible options. It is then mentioned that there are 10 possible options and the correct answer is 0.19. The conversation concludes by emphasizing the importance of considering all possible options and the probability of achieving a specific sequence.
  • #1
Dell
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0
we throw a dice 5 times,
what is the probability of throwing the same number exactly 3 times?

i tried using all kinds of techuniques but can't seem to get this,

if A is a given number and X is any other number

A* A* A* X* X
6* 1* 1* 5* 5 =150

150/6^5=0.0192901

but that doesn't take into account any other options, for example A*X*A*X*A, X*A*A*X*A ...

so then i thought since i can either roll a given number or not, and the possibility that i will is 1/6

X~B(5,1/6)

P(X=3)=5C3*(1/6)^3*(5/6)^2=0.03215

the correct answer is 0.19,- which makes me think my 1st attempt was correct and there are 10 options, but how do i find these options and also, why is the binomial incorrect??
 
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  • #2


If you take one possible sequence as you've done, giving AAAXX with A being the number of choice, what is the probability of achieving this sequence? How many other possibilities are there to mix up the order of the above sequence, such as AAXAX etc. ? And finally, how many possible numbers for A are there?

The same result can be achieved by the binomial distribution method.
 
  • #3


thanks i got it, i found the probability of a cerain number 3 times, i need to multiply by 6
 
  • #4


You got to love those silly mistakes :biggrin:
 

1. What is the significance of throwing the same number exactly 3 times?

The significance of throwing the same number exactly 3 times is that it is a specific outcome in a probability experiment. It can be used to calculate the probability of an event occurring multiple times in a row.

2. Can you explain the concept of probability in relation to throwing the same number 3 times?

Probability is the likelihood of a specific outcome occurring in a given situation. In the case of throwing the same number exactly 3 times, the probability can be calculated by taking the number of ways the outcome can occur (in this case, one) and dividing it by the total number of possible outcomes (in this case, six).

3. Is the probability of throwing the same number 3 times different from throwing any other combination of numbers?

Yes, the probability of throwing the same number exactly 3 times is different from throwing any other combination of numbers. This is because the specific outcome of throwing the same number 3 times has a lower probability compared to other outcomes, such as throwing a different number each time.

4. How does the number of dice used in the experiment affect the probability of throwing the same number 3 times?

The number of dice used in the experiment does not affect the probability of throwing the same number exactly 3 times. The probability is solely based on the specific outcome and the total number of possible outcomes.

5. Is it possible to increase the probability of throwing the same number 3 times by changing the type of dice used?

No, changing the type of dice used will not affect the probability of throwing the same number exactly 3 times. The probability is determined by the outcome and the total number of possible outcomes, not the type of dice.

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