MHB Dice Probability: 5 Rolls, Increasing Number

  • Thread starter Thread starter juantheron
  • Start date Start date
  • Tags Tags
    Dice Probability
AI Thread Summary
The probability of rolling a higher number than the previous roll in five consecutive dice rolls is calculated by considering the unique increasing sequences possible with six outcomes. Since all rolls must be different, there are exactly six valid increasing sequences. The total number of possible sequences for five rolls is \(6^5\). Thus, the probability is determined by the ratio of the six increasing sequences to the total possible sequences. This results in a clear understanding of the likelihood of achieving such an outcome in five rolls.
juantheron
Messages
243
Reaction score
1
A Dice is Rolled $5$ times. The Probability of Getting a higher number then the previous number each time is
 
Mathematics news on Phys.org
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
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
View full post »

Thread 'Six Pencil Puzzle'

Is it possible to arrange six pencils such that each one touches the other five? If so, how? This is an adaption of a Martin Gardner puzzle only I changed it from cigarettes to pencils and left out the clues because PF folks don’t need clues. From the book “My Best Mathematical and Logic Puzzles”. Dover, 1994.
View full post »
Thread 'Imaginary Pythagoras'

Thread 'Imaginary Pythagoras'

I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
View full post »

Similar threads

MHB Probability of Rolling Sum > 3 with Two Dice
Replies
5
Views
3K
MHB Find the probability all 5 dice rolls are the same
Replies
2
Views
4K
MHB Understanding Dice Throwing Probabilities: A Layman's Guide
Replies
8
Views
4K
MHB Probability of AT LEAST 3 6s in 5 Dice Rolls
Replies
1
Views
5K
MHB Pr of exactly one dice showing 2
Replies
9
Views
2K
MHB What is the probability that at least 5 was shown for 5 or more times?
Replies
4
Views
1K
I What Is the Probability of Getting a Specific Number When Throwing Three Dice?
Replies
5
Views
1K
MHB Dice rolling -Which of 2,6,1006 is more likely to be one of these totals?
Replies
8
Views
2K
MHB How Many Rolls of Dice to Get Sum 12?
Replies
5
Views
2K
MHB How Do You Calculate Expected Value in a Dice Game?
Replies
2
Views
7K

Hot Threads

Recent Insights

Back
Top