Dice Probability: 5 Rolls, Increasing Number

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SUMMARY

The probability of rolling a die 5 times and obtaining an increasing sequence of numbers is calculated by considering the total number of possible outcomes and the specific increasing sequences. With 6 possible outcomes from a die, there are exactly 6 increasing sequences of 5 rolls. The total number of sequences when rolling a die 5 times is \(6^5\). Therefore, the probability of achieving an increasing sequence is \( \frac{6}{6^5} = \frac{1}{1296} \).

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A Dice is Rolled $5$ times. The Probability of Getting a higher number then the previous number each time is
 
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It's easy to explicitly enumerate all increasing sequences of 5 numbers from {1, ..., 6}.
 
jacks said:
A Dice is Rolled $5$ times. The Probability of Getting a higher number then the previous number each time is

Because the sequences are increasing all the die rolls are different, as there are only 6 possible outcomes all but one of the outcomes must be present in such a sequence and there is only one order that these can be in, so there are exactly \(6\) increasing sequences of 5 die roll outcomes from a total of \(6^5\) possible sequences of 5 die roll outcomes...

CB
 

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