Respuesta :
Answer:
a) 1,679,616 sequences
b) 6,561 sequences
c) 46,656 sequences
Step-by-step explanation:
a) How many different sequences are possible?
For each of the 8 dice, there are 6 possible outcomes. Therefore, the total number of difference sequences is:
[tex]6^8=1,679,616\ sequences[/tex]
b) How many different sequences consist entirely of even numbers?
For each of the 8 dice, there are 3 possible even outcomes. Therefore, the total number of difference sequences is:
[tex]3^8=6,561\ sequences[/tex]
c) How many different sequences are possible if the first, third, and fourth numbers must be the same?
If the first, third and fourth numbers are fixed, there are only 5 "free" positions, while there are 6 possible outcomes for the fixed positions since they have to be the same
[tex]6*6^5 = 46,656\ sequences[/tex]
(a) The possible different sequence is [tex]6^8=1,679,616[/tex]
(b) The possible different sequence entirely of even numbers
[tex]3^8=6,561[/tex]
(c)The possible different sequence, if the first, third, and fourth numbers must be the same [tex]6 \cdot 6^5=46,656[/tex]
Possible outcome
Possible outcome of a 6-sided die when it is rolled 'n' times is [tex]6^n[/tex]
Given information
A fair 6-sided die is rolled 8 times and the resulting sequence of 8 numbers is recorded.
(a) 6- sided dice is rolled 8 times
The possible different sequence is [tex]6^8=1,679,616[/tex]
(b) The sequence consist entirely of even numbers
There are 3 even numbers in 6-sided dice. Even numbers are 2,4,6
There are 3 possible even outcomes.
The possible different sequence entirely of even numbers
[tex]3^8=6,561[/tex]
(c) the first, third, and fourth numbers must be the same
When the first , third and fourth numbers are fixed then there is only one possibility. For the remaining free positions there are 6 possible outcomes .
The possible different sequence, if the first, third, and fourth numbers must be the same [tex]6 \cdot 6^5=46,656[/tex]
Learn more information about possible outcomes here:
brainly.com/question/21207761
