What is the probability that in toasing a dice for six times ...?

Question

2)first two number the same?

3)only geting two same number?

with details please

Answer 1

Sample space  S = { (1,1,1,1,1,1), ( 1,1,1,1,1,2) .....

..... ( 6,6,6,6,6,6,) }

n(S) = 6^6

a) first two numbers the same

number of ways of choosing the first two numbers the same

= The same number can be chosen in 6 ways ( any of 1 to 6)  AND

the remaining 4 places can be filled in 6P4 (P=permutation) ways ( no. of arrangements of 6 things in 4 places)

= 6* (6P4)

Probability of first two numbers same = 6* (6P4) / (6^6)

=6*360/ (6^6)

=5/108

b) only geting two same number

no. of ways of selecting the same number = 6  ( as above , any of 1 to 6)

no.of ways of selecting the position of the identical number = 6C2 (C= Combination) = 15

no. of ways of filling remaining 4 places = 5P4 ( the previously selected number should be omitted , as it cannot repeat as per question) = 120

So , no. of ways getting only two numbers same = 6* 15 * 120 =10800

Therefore , required probability =  10800/ (6^6) = 25/108

Answer 2

Probably of tossing a 6-sided die

To get one of the numbers on the first toss of a die is 6/6 or 1

To get the same number of the second toss is 1/6  

[answer 2]

The probability of not getting that number on the following 3 rolls is (5/6)^3 = 125/216

That gives total proability is 1*1/6*125/216 = 125/1296

=0.0964... [used calculator] rounded up it is about 10%

[answer 3 if the first 2 are the same]

Answer 3

Your question is spelled wrong btw its, "tossing" and

What type of dice? 6 sided, 4 sided, etc..

If its a 6 sided dice, and you toss is 6 times.

Probability for any number is 1/6.

Anyways, I can't understand the question, please rewrite it.

"

2)first two number the same?

3)only geting two same number?

"

Answer 4

2)first two number the same?

so the first one can be any number

second one must be the same  

answer = 1/6

3)only geting two same number?

the question is not clear

is it means something like AABCDE , ABCDCE,.... ?

so you have to say exactly one pare of ident. number

in this case

P(x) = (6 over 2) * 1* 1/6 * 5/6 * 4/6 * 3/6 * 2/6

= 15* 1/6 * 5/6 * 2/3 * 1/2 * 1/3

= 75/ 324 = 25/108