Question

A six-sided die of unknown bias is rolled 20 times, and the number 3 comes up 6 times. In the next three rounds (the die is rolled 20 times in each round), the number 3 comes up 6 times, 5 times, and 7 times.
The experimental probability of rolling a 3 is %, which is approximately % more than its theoretical probability. (Round off your answers to the nearest integer.)

Answer 1

so 24/80 = 30%
So the experimental probability is 30 %

Answer 2

The theoretical probability is 1/20+1/20+1/20+1/20=1/5=20%

Answer 3

The experimental probability of rolling a 3 is 30%, which is approximately ????% more than its theoretical probability.
This isn't right. :(

Answer 4

@mathstudent55 can you help me

Answer 5

@mathstudent55 do you know how to do this?

Answer 6

@Michele_Laino can u help please?

Answer 7

here we have to apply the binomial distribution

Answer 8

for example the probability to get the number 3, five times, after 20 rolls, is given by the subsequent formula:
\[\Large probability = \left( {\begin{array}{*{20}{c}}
{20} \\
5
\end{array}} \right) \times {\left( {\frac{1}{6}} \right)^5} \times {\left( {\frac{5}{6}} \right)^{20 - 5}}\]
where:
\[\Large \left( {\begin{array}{*{20}{c}}
{20} \\
5
\end{array}} \right) = \frac{{20!}}{{5!\left( {20 - 5} \right)!}}\]

Answer 9

sorry i had stepped away

Answer 10

and that probability has to be compared with the experimental probability, which is:
5/20, as I can read from the text of your exercise

Answer 11

so you have to compute this:
\[\Large probability = \left( {\begin{array}{*{20}{c}}
{20} \\
5
\end{array}} \right) \times {\left( {\frac{1}{6}} \right)^5} \times {\left( {\frac{5}{6}} \right)^{20 - 5}} = ...?\]
you can use Windows calculator, for example

Answer 12

5/20 would be 25% yes

Answer 13

is my answer for experimental correct?
30%

Answer 14

or am I confusing the 2

Answer 15

the experimental probability is right, since it is 5/20=25%. Nevertheless we have to compute the theoretical probability, which is gioven by the subsequent formula:
\[\Large probability = \left( {\begin{array}{*{20}{c}}
{20} \\
5
\end{array}} \right) \times {\left( {\frac{1}{6}} \right)^5} \times {\left( {\frac{5}{6}} \right)^{20 - 5}} = ...?\]

Answer 16

given*

Answer 17

do you know how to compute that quantity?

Answer 18

yes its the six side die
there are 4 rounds of 20 and the rolls add up to 6+6+5+7= 24
so 24/80 =30%
yes

Answer 19

that's right! that is the experimental probability

Answer 20

now we have to compute the theoretical probability

Answer 21

this I am confused because I thought I was doing it right but the number comes out less than it should be

Answer 22

no, please the experimental probability, namely 24/80 is right!

Answer 23

i just reread the questions and think I was reading it wrong :P

Answer 24

the most part of work, is to compute the theoretical probability, using the binomial distribution

Answer 25

sorry either having problems with open study or internet. keep getting the uh oh owl

Answer 26

the theoretical probability, is given by the sum of the single probabilities, namely:
\[\Large \begin{gathered}
\left( {\begin{array}{*{20}{c}}
{20} \\
5
\end{array}} \right) \times {\left( {\frac{1}{6}} \right)^5} \times {\left( {\frac{5}{6}} \right)^{20 - 5}} + \hfill \\
\hfill \\
+ 2 \times \left( {\begin{array}{*{20}{c}}
{20} \\
6
\end{array}} \right) \times {\left( {\frac{1}{6}} \right)^6} \times {\left( {\frac{5}{6}} \right)^{20 - 6}} + \hfill \\
\hfill \\
+ \left( {\begin{array}{*{20}{c}}
{20} \\
7
\end{array}} \right) \times {\left( {\frac{1}{6}} \right)^7} \times {\left( {\frac{5}{6}} \right)^{20 - 7}} = ...? \hfill \\
\end{gathered} \]

Answer 27

5/20=25%
which would make the final answer
The experimental probability of rolling a 3 is 30%, which is approximately 10% more than its theoretical probability.

Answer 28

Is this correct

Answer 29

help!!!

Answer 30

isnt the theoretical probability of rolling a 3 just 1/6?

Answer 31

yes that is correct

Answer 32

then the percent of error is just how far off we are ...

3/10 - 1/6
----------
1/6

Answer 33

but it is rolled 80 times

Answer 34

the theorectical probability is 1/6 regardless of the number of times its rolled ..

Answer 35

the answer would be 4/5

Answer 36

is that from an answer key?

Answer 37

no I have no answer key

Answer 38

im trying to fiqure out how to do it but keep getting more confused

Answer 39

spose i guess that ill have 10 presents for christmas, and i get 8

what is the percent of my error?

2 out of 8 = 1/4 or 25%

is this a valid approach?

Answer 40

yes

Answer 41

each roll of the die i only have 1/6 to get a 3

Answer 42

from the google ...

Percent error -- take the absolute value of the error divided by the theoretical value, then multiply by 100.

Answer 43

|3/10 - 1/6| is the absolute difference between observed and theoretic

1/6 is the theoretic

Answer 44

is that 2/15

Answer 45

1.8 - 1 = .8

Answer 46

\[\frac{\dfrac{3}{10}-\dfrac{1}{6}}{\dfrac{1}{6}}\]
\[\frac{6}{6}*\frac{\dfrac{3}{10}-\dfrac{1}{6}}{\dfrac{1}{6}}\]
\[\frac{\dfrac{18}{10}-\dfrac{6}{6}}{\dfrac{6}{6}}=1.8-1\]

Answer 47

Im confused where you got the 1.8

Answer 48

why, i wrote it all out ...

Answer 49

.8

Answer 50

tell me where i got 1.8 from

Answer 51

im not sure tried to fiqure that out

Answer 52

wll we start with the setup

3/10 - 1/6
----------
1/6

we good here? this make sense?

Answer 53

yes ok the same 4/5

Answer 54

1.8 =4/5

Answer 55

i dont like dividing by 1/6, id rather divide by 1

6*1/6 = 6/6 = 1 soo, let multiply the whole thing by 6/6


6(3/10 - 1/6)
----------
6/6

now since we are dividing by 1, the bottom is irrelevant

6(3/10 - 1/6)

distribute

18/10 - 6/6

simplify

1.8 - 1

Answer 56

.8

Answer 57

1.8 is not equal to 4/5 you cant be almost 2 and be less than 1

Answer 58

1.8 = 1 + 4/5 if thats how you want to see it

Answer 59

.8 = 4/5 but thats not a percent of error, 80% is a percentage

Answer 60

no matter what I do I keep coming up with 4/5. Is the error the differnce like 20%

Answer 61

no, the error is 4/5, or 8/10 or .80 ....

.80 * 100 = 80, for 80%

Answer 62

another way to approach this is

we rolled 23, we expected 80/6 = 13

(23 - 13)/13 = .769, or about 77% which is close to 80% depending on how you work the numbers

Answer 63

If it is 80% it doesn't make sense to me because I thought the percentage was less than 305 because of the way the question reads

Answer 64

less than 30%

Answer 65

how do we define percent of error?

Answer 66

100 * (actual - theory)/ theory

do we agree with this?

Answer 67

100*(3/10 - 1/6)(1/6)

Answer 68

whatever that value is, is our percentage of error

Answer 69

and that value is 80 correct

Answer 70

yes, we calculated that already

or, if we are to use the rolls instead: 80/6 = 13.3333 and its rather impossible to have .333 of a roll, so 13 rolls are expected.

100 * (24 - 13)/13

Answer 71

how you work the problem is up to you, so choose one and stick with it :)

Answer 72

ok thanks