## mathdummy4 3 years ago PLEASE HELP a dice is rolled 8 times. find the probability. p(getting at least 7 even numbers) a. 1/256 b. 9/256 c. 1/32 d. 1/16

1. mathdummy4

any ideas?

2. ganeshie8

total number of permutations when a dice is rolled 8 times = 6^8

3. WLB250219

$3/48$= x

4. ganeshie8

even numbers : 2, 4, 6 so, out of 8 times u perform experiment, 7 times - u have 3 choices : 3^7 one time you have 6 choices : 6 total permutations in favor = 3^7 * 6

5. mathdummy4

how did you get 3/48??

6. mathmate

At least 7 even is the same as at most 1 odd. 0 odd = 1/256 1 odd = 8/256 Total = 9/256

7. ganeshie8

p(getting at least 7 even numbers) = $$\frac{3^7*6}{6^8}$$ = $$\frac{3^7}{6^7}$$ = $$\frac{3^7}{3^7.2^7}$$ =$$\frac{1}{2^7}$$ =$$\frac{1}{256}$$

8. WLB250219

there are 3 even numbers on a dice and 3 odd and you dividethe 3 even by 8 times and that will give you the answer

9. WLB250219

6times 8 is 48 and divide by 3 and you will get 16 so the answer is 1/16

10. mathdummy4

okay...so what if you were looking for 8 odd numbers? wouldn't it be the same process?

11. WLB250219

yes

12. mathdummy4

well i got the same answer..1/16...is that right?

13. WLB250219

yes

14. mathmate

Binomial distribution: P(n,i)=(n,i)p^i q^(n-i) (n,i)=n!/(i!(n-i)!) Here, p=q=1/2 (8,0)=1 (8,1)=8 (8,2)=8*9/2=36, ... So any number of even or odd can be calculated.

15. eliassaab

You have to have 7 throws even and the 8th one can be either. $\frac 1{2^7} 8=\frac 1 {16}$

16. eliassaab

You multiply by 8 to count where the even or odd throw is.

17. WLB250219

|dw:1344014586415:dw|yes

18. mathdummy4

thanks:)

19. WLB250219