Question

PLEASE HELP a dice is rolled 8 times. find the probability. p(getting at least 7 even numbers)
a. 1/128
b. 7/32
c. 1/32
d. 1/16

Answer 1

my explanation was that there are 48 outcomes
and there are 3 even nos. that we want 7 times
so 7 x 3 = 21
Final ans = 21/48

Answer 2

obviously it is wrong
pls explain where i am going wrong

Answer 3

at least 7 means, P(7) or P(8) or P(9) or ....

so, what is the probability of getting 7 even numbers ... what is the probability of getting 8 even numbers? then add the results

Answer 4

do you know how to do i binomial probability?\[\binom{n}{k}p^kq^{n-k
}\]

Answer 5

no

Answer 6

hmmm, well do you know the probability of getting an even or odd number on 1 roll of the dice?

Answer 7

.5 ?

Answer 8

yes

Answer 9

now, if we setup an 8 roll situation we get:

eeeeeeeo, 7 even and 1 odd

how many ways are there to permute this arrangement? in other words, how many ways can we resort this?

Answer 10

1 eeeeeeeo
2 eeeeeeoe
3 eeeeeoee
4 eeeeoeee
5 eeeoeeee
6 eeoeeeee
7 eoeeeeee
8 oeeeeeee

i count 8 ways that we can arrange the setup.

so 8 times, .5^7 * .5^1

this gives us the probability of rolling 7 even numbers out of 8 rolls

Answer 11

so 8 times, .5^7 * .5^1 ? this part makes no sense

Answer 12

do you agree that there are 8 ways to arrange how the outcome of the dice happen in order to get us 7 even numbers and 1 odd number?

Answer 13

yes

Answer 14

all thats left to do is determine the probability of getting: an even, and an even, and an even, and an even, and an even, and an even, and an even, and an odd.

P(even) and P(even) and P(even) and P(even) and P(even) and P(even) and P(even) and P(odd)

or written another way

P(even) * P(even) *P(even) *P(even) *P(even) *P(even) *P(even) *P(odd)

or better yet, since P(even) = P(odd) = .5

.5 * .5 * .5 * .5 * .5 * .5 * .5 * .5

Answer 15

ok

Answer 16

so, 8 ways to get: .5^7 * .5^1
7 even and 1 odd

Answer 17

yes

Answer 18

P(7even and 1 odd): 8*.5^8

and there is only 1 way to get 8 even so

P(8even and 0odd) = 1*.5^8


the probability of getting one or the other is just the sum of them together

8*.5^8 + .5^8. but since your options are in fractions it might be best to use 1/2 instead of .5

Answer 19

so what is the final ans?

Answer 20

(1/2)^8

Answer 21

@amistre64

Answer 22

the final answer is: 8*.5^8 + .5^8, simplify to your hearts content

Answer 23

8/2^8 + 1/2^8 = 9/2^8

Answer 24

C ? or B ?

Answer 25

which one is equal to 9/2^8?

Answer 26

since 9 and 2^8 have no common factors .... id pick the one with a 9 up top :/

Answer 27

which choice is it now??

Answer 28

i wrote my choices incorrectly last time

Answer 29

... sigh. why did you change them?

Answer 30

http://www.wolframalpha.com/input/?i=8%2F2%5E8+%2B+1%2F2%5E8