Question

A dies is thrown six times.

(a) what is the probability that the nth throw is n on each occasion?

(b) what is the probability that the nth throw is n on exactly five occasions?

Answer 1

the first answer is (1/6)^6...

Answer 2

i am not quite sure of the 2nd.. bu i think its (1/6)^5*(5/6).. Still you can confirm with someone..

Answer 3

Wait, I misread the question.

Answer 4

can you help me out with part (b)

Answer 5

How many sides does the dice have? n?

Answer 6

Or just 6?

Answer 7

just 6

Answer 8

So what do you mean by "the nth throw is n"?

Answer 9

the number on the die is the same number as the throw

Answer 10

Oh, ok.

Answer 11

like first throw you get 1. i think thats what it means lol

Answer 12

So for every throw there is a probability of 1/6 of getting the right number.

Answer 13

Thomas9 i believe the first one is correct..
they are independent events.. everytime the probability is 1/6 so you just multiply the probabilities according to multiplication principle

Answer 14

yeah

Answer 15

first one is indeed correct.

Answer 16

the first one is right but the second one isnt

Answer 17

oh...

Answer 18

i have the answer its 5/7776

Answer 19

but im not sure how to get it

Answer 20

It's binomial distributed, so you need to fill in the pdf.
http://www.wolframalpha.com/input/?i=binomial+distribution+pdf

Answer 21

n is the number of expirements, it's 6 in this case because we throw 6 times.

Answer 22

p is the probability of succes, 1/6 in this case.

Answer 23

and x is number of times of succes, in this case 5.

Answer 24

\[P(X=5)=\left(\begin{matrix}6 \\ 5\end{matrix}\right)\frac{1}{6}^5\frac{5}{6}^{6-5}=6\frac{1}{6}^5\frac{5}{6}=\frac{5}{6^5}\]

Answer 25

I hope that made sense to you.

Answer 26

ok wait lol is there a multiplication inbetween each one?

Answer 27

yes

Answer 28

\[P(X=5)=\left(\begin{matrix}6 \\ 5\end{matrix}\right)\cdot\frac{1}{6}^5\cdot\frac{5}{6}^{6-5}=6\cdot\frac{1}{6}^5\cdot\frac{5}{6}=\frac{5}{6^5}\]

Answer 29

k thanks heaps:)