dice probability

[alexmsantos]

Hello guys,





I have a doubt of probability, follows below:



I have a dice with 20 sides and I need to hit the sequence



1,2,3,4,5,6





this is ok (20x19x18x17x16x15 / 6X5X4X3X2X1) = 38,760



the probability of hitting the sequence of 6 random numbers is 1 in 38,760



but how to calculate the probability of hitting 5 numbers out of 6? And 4 numbers out of 6?



I mean, I will throw the dice 6 times and hit 5 numbers

or throw the dice 6 times and hit 4 numbers, how to calculate the probability of hit?





other probability doubt is



I have 5 holes and 2 squirrels





squirrels may appear in the holes:



1 and 2

1 and 3

1 and 4

1 and 5



2 and 3

2 and 4

2 and 5 and so on



how to make this calculation to get the exact number of probability



Thanks

 

[Romsek]

You say you need to hit the sequence 1,2,3,4,5,6. I take that to mean you need to hit them in that order.
Assuming the dice rolls are independent of one another and that this is a fair 20 sided die then the probability of hitting this sequence is

[MATH]p=\left(\dfrac{1}{20}\right)^6[/MATH]
I don't know what you're asking about the squirrels.

 

[Mr. Bland]

Welcome to Free Math Help!

I have a dice with 20 sides and I need to hit the sequence

1,2,3,4,5,6

this is ok (20x19x18x17x16x15 / 6X5X4X3X2X1) = 38,760

the probability of hitting the sequence of 6 random numbers is 1 in 38,760

It looks like you're trying to roll a specific sequence of length 6? For each roll here, you have a [MATH]\frac{1}{20}[/MATH] chance of rolling the "correct" number, so the likelihood of rolling the correct number 6 rolls in a row is:

[MATH]\left(\frac{1}{20}\right)^6 = \frac{1}{64000000}[/MATH]​

but how to calculate the probability of hitting 5 numbers out of 6? And 4 numbers out of 6?

I mean, I will throw the dice 6 times and hit 5 numbers

or throw the dice 6 times and hit 4 numbers, how to calculate the probability of hit?

Take the likelihood of the outcome for each roll and multiply everything together. The chance of "hitting" a number is [MATH]\frac{1}{20}[/MATH], and the chance of "missing" a number is [MATH]\frac{19}{20}[/MATH]. If you're looking for 4 hits and 2 misses, you'd do something like this:

[MATH]\left(\frac{1}{20}\right)^4 * \left(\frac{19}{20}\right)^2 = \frac{361}{64000000}[/MATH]​

I have 5 holes and 2 squirrels

squirrels may appear in the holes:

1 and 2
1 and 3
1 and 4
1 and 5

2 and 3
2 and 4
2 and 5 and so on

how to make this calculation to get the exact number of probability

What probability are you trying to find? The likelihood that a specific pair of holes contains squirrels?

 

[alexmsantos]

You say you need to hit the sequence 1,2,3,4,5,6. I take that to mean you need to hit them in that order.
Assuming the dice rolls are independent of one another and that this is a fair 20 sided die then the probability of hitting this sequence is

[MATH]p=\left(\dfrac{1}{20}\right)^6[/MATH]
I don't know what you're asking about the squirrels.

Hi Romsek

Thanks for answer

Don't need to be in a row, could be any sequence since hit the number (1,2,3,4,5,6)
I play the dice 6 times and i have 1 chance in 38,760 to pick up the combination that o chose, but how is the odds to get 5 numbers and 4 numbers?
I mean, i randomly chose the sequence (1, 8, 9, 12, 15, 20). How is the odds to get 5 numbers from those 6? And 4 numbers?

About the squirrels

How many time the squirrels could be in the wholes. I will do manually

x = squirrels
0 = whole


XX000
X0X00
X00X0
X000X
0XX00
0X0X0
0X00X
00XX0
00X0X
000XX

10 times

I don't know how to is the formule to calculate that.

thanks gain

 

[alexmsantos]

Welcome to Free Math Help!


It looks like you're trying to roll a specific sequence of length 6? For each roll here, you have a [MATH]\frac{1}{20}[/MATH] chance of rolling the "correct" number, so the likelihood of rolling the correct number 6 rolls in a row is:

[MATH]\left(\frac{1}{20}\right)^6 = \frac{1}{64000000}[/MATH]​

Take the likelihood of the outcome for each roll and multiply everything together. The chance of "hitting" a number is [MATH]\frac{1}{20}[/MATH], and the chance of "missing" a number is [MATH]\frac{19}{20}[/MATH]. If you're looking for 4 hits and 2 misses, you'd do something like this:

[MATH]\left(\frac{1}{20}\right)^4 * \left(\frac{19}{20}\right)^2 = \frac{361}{64000000}[/MATH]​

What probability are you trying to find? The likelihood that a specific pair of holes contains squirrels?

Hi Mr Bland


Don't need to be in a row

Imagine a lottery game and you can get the jackpot if hit the 6 number from 20, but you can get small prize if get 5 number and 4 number? How is the formule to know the odds to get 5 numbers and 4?


About the squirrels

How many time the squirrels could be in the wholes. I will do manually

x = squirrels
0 = whole


XX000
X0X00
X00X0
X000X
0XX00
0X0X0
0X00X
00XX0
00X0X
000XX

10 times

I don't know how to is the formule to calculate that.

 

[Dr.Peterson]

I've edited the question to make it easier to read (note that "dice" is a plural, but you only have one, a "die"):

Hello guys,

I have a doubt of probability, follows below:

I have a die with 20 sides and I need to hit the sequence

1,2,3,4,5,6​

this is ok (20x19x18x17x16x15 / 6X5X4X3X2X1) = 38,760
the probability of hitting the sequence of 6 random numbers is 1 in 38,760

but how to calculate the probability of hitting 5 numbers out of 6? And 4 numbers out of 6?
I mean, I will throw the die 6 times and hit 5 numbers
or throw the die 6 times and hit 4 numbers, how to calculate the probability of hit?

other probability doubt is
I have 5 holes and 2 squirrels
squirrels may appear in the holes:

1 and 2​

1 and 3​

1 and 4​

1 and 5​

​

2 and 3​

2 and 4​

2 and 5 and so on​

how to make this calculation to get the exact probability

Thanks

A few things need clarification.

First, you apparently want to roll 1, 2, 3, 4, 5, 6 in that order, right? But the die is not restricted to rolling different numbers, so a permutation is not appropriate. As others have said, the number of sequences can you get in 6 rolls is 20⁶, not ₂₀P₆.

Second, it is not clear what you mean by "hitting 5 numbers out of 6". You apparently want the probability that 5 of 6 rolls will match a number specified for that roll (e.g. 1 for the first roll, 2 for the second, ..., and all but one is the number you want). Have you learned about the binomial distribution? This was almost described in post #3, but the work shown is incorrect. Please search for information on this topic.

Third, you asked for probability in the squirrel problem, but your answer in post #5 seems to ask instead for the number of possibilities. This is a combination problem. Have you learned about that? It is ₅C₂, the number of combinations of 5 items taken 2 at a time.

Here are sources for the three topics you need:

• https://www.mathsisfun.com/combinatorics/combinations-permutations.html
• https://www.mathsisfun.com/data/binomial-distribution.html