Question

Can somebody help me with Bernoulli Trials?

Answer 1

ask!

Answer 2

The question asks:
Consider tossing a fair die 16 times. Find the value or values of k such that the probability the number 2 comes up exactly k times is as large as possible.

i said (n+1)p = 17/6 so k =\[\lfloor 17/6 \rfloor\]

and i was marked wrong

Answer 3

so if X is the number of twos you see, you want to maximimize
\[P(X=k)\] right?

Answer 4

i think k stands for number of trials so after how many trials will two have the highest probability?

Answer 5

the probability you get k twos in 16 trials is
\[\dbinom{16}{k}(\frac{1}{2})^{16}\] right?

Answer 6

so the question boils down to "what is the k that maximized \(\binom{16}{k}\)?"

Answer 7

oh crap i was thinking about coins hold on that is utterly wrong!!!

Answer 8

you want to maximize
\[\dbinom{16}{k}(\frac{1}{6})^k(\frac{5}{6})^{16-k}\]

Answer 9

yeah but that's basically it with dice. for what k will the prob. be greatest. my textbook said something along the lines of (n+1)p

Answer 10

sorry ignore first post it was way off

Answer 11

but i put that and got it wrong

Answer 12

well let us check
i am not sure what your answer means, but it should be 2 or three

Answer 13

i forget, is it floor \(\frac{17}{2}=2\) or ceiling \(\frac{17}{2}=3\)?

Answer 14

what did you write as an answer? your number needs to be an integer

Answer 15

7 since it was\[\lfloor 17/6 \rfloor\]

Answer 16

i mean 2***

Answer 17

oh ok lets check

Answer 18

\[P(X=2)=.2566\]
\[P(X=3)=.2423\]
so it looks like you are a winner

Answer 19

hmm i guess my professor made a mistake by marking me wrong i will have to speak with him but thanks for helping! =D

Answer 20

oh but you said you were marked wrong. i would put that down to human error, not your error

Answer 21

yeah say very politely "i went over my exam to check all my mistakes and make sure i understood the material, but when i checked my answer i looked like i was correct? can you help explain?"