Question

A coin is unbalanced such that it comes up tails 55% of the time. In an effort to prove that the coin is unfair, an experimenter flips the coin 50 times.
a) what is the probability that the coin comes up tails more than 25 times?
b) what is the probability that the coin comes up tails more than 30 times?
c) what is the probability that the coin comes up tails exactly 25 times?

Answer 1

@jim_thompson5910 how would I figure this out?

Answer 2

you all figure out that calculator? here is one way to do it
http://www.wolframalpha.com/input/?i=%2820+choose+3+%29*%281%2F6%29^3%285%2F6%29^17

Answer 3

yes we did and thanks for that, wolfram is usually a quicker way to compute

but it's also handy to know how to do it on a calculator so you can do it on the test

Answer 4

as for this newest one, this is definitely going to be a pain to do by hand

Answer 5

for part a) you have to calculate the binomial probabilities for k = 26, k = 27, k = 28, ..., k = 50 and add them all up

the good news is that your calculator supports the binomial cdf function

Answer 6

i thought maybe this was a statistics question, use the normal approximation to the binomial
otherwise it is going to be a real drag
i am not that good at those problems, so i will be quite now
but as i said, my best guess is normal approximation

Answer 7

I guess you could do that, but if you use the normal distribution, you have to use the Continuity Correction Factor

Answer 8

So what do I do?
*Sorry OpenStudy crashed and I had to switch computers which required some negotiating*

Answer 9

that's ok

Answer 10

do you know how to use the binomial cdf function?

Answer 11

on your calculator

Answer 12

What's that?

Answer 13

before, we calculated the binomial pdf (basically a single probability)

now, we want to calculate a whole bunch of probabilities (from k = 26 to k = 50) and add them up. That gives the binomial cdf

Answer 14

we could do what we did in the last problem, and do k = 26, k = 27, ..., k = 50

but that's very tedious

the good news is that there's a much quicker way using a calculator

Answer 15

are you able to find the distribution button?

Answer 16

Where is that? Do I get to it the same way I got to the last one?

Answer 17

let me look at the manual again

Answer 18

are you able to get into stat mode?

Answer 19

Yes

Answer 20

ok go ahead and get into stat mode, then press f5 to bring up the DIST (distribution) menu

Answer 21

Okay, now what?

Answer 22

then select BINM (for binomial)

Answer 23

what do you see after you do this?

Answer 24

There's then the options: Bpd, Bcd, and InvB

Answer 25

ok one sec

Answer 26

do Bcd (Binomial Cumulative Distribution)

Answer 27

the first one would have solved the previous problem in basically one step

Answer 28

Now what?

Answer 29

whats on your screen right now?

Answer 30

the calculator screen

Answer 31

Data: List
List: List1
Numtrial: 0
P: 0
Execute

Answer 32

ok for Numtrial, you're going to put in 50 (since there are 50 coin tosses, so 50 trials)

Answer 33

p = 0.55 because this is the probability of landing on tails (for this coin)

Answer 34

Alright

Answer 35

as for the "data" portion, I'm not sure

Answer 36

are you able to change "list" to something else?

Answer 37

I clicked on 'list' and this popped up:
Select List No.
List [1~26]:

Answer 38

so you can only choose from list1 through list26

Answer 39

I wish there was a way to input a single value (and forget about the list)

Answer 40

Oh!
You can change 'Data: List' to 'Data: Variable'
and then 'List: List1' changes to 'x: 0'
is that helpful?

Answer 41

oh much better

Answer 42

that x would then be 25 (for part a)

Answer 43

it might not give the final answer, but it certainly will help get us there

Answer 44

so try

x = 25
Numtrial = 50
p = 0.55

and tell me what you get

Answer 45

Binomial C.D
p = 0.28396067

Answer 46

So what that just calculated was P(X <= 25)

basically the probabilities for k = 0, k = 1, ..., k = 25

Answer 47

but we want k = 26 on up to k = 50

Answer 48

so we simply subtract from 1 to get

1 - 0.28396067 = 0.71603933

Answer 49

Ohh, so that's a?

Answer 50

yes and do you see why I subtracted from 1?

Answer 51

Yes. So for b, would I do the same thing except with 30 instead of 25 and subtract that number from 1?

Answer 52

exactly

Answer 53

you would use a calculator to compute P(X <= 30)

then subtract from 1 to get P( X > 30)

Answer 54

Is 0.19736794 correct?

Answer 55

let me check

Answer 56

I'm getting the same (more or less), nice work

Answer 57

Yay!

Answer 58

to answer part c), you can either


use the formula (n C r)*(p)^(k)*(1-p)^(n-k)

OR

you can use the Bpd portion (instead of the Bcd) of the calculator

Answer 59

Bpd calculates single probabilities

Bcd calculates a whole bunch of what Bpd does and adds them all up

Answer 60

oops I meant to say (n C k)*(p)^(k)*(1-p)^(n-k)

Answer 61

would it be 0.08733002?

Answer 62

correct

Answer 63

Awesome! :D