Question

Reece and Kala are playing a game with a die. As Reece rolls the die, Kala notices that it seems to land on the number 6 a lot. She notes that for 5 out of 10 rolls of the die, the die comes up as a 6.


The binomial probability of rolling five 6s out of ten throws is approximately _____. The experimental probability of rolling a 6 is _____.


Determine the values that accurately complete the previous two sentences. Then use those values to help choose an answer to the following question.


Should Kala doubt whether the die is a fair die?

Answer 1

- Kala might doubt whether the die is a fair die, since the experimental probability of rolling that many 6s is much greater than the binomial probability. However, since there were only 10 experiments, the die still may be fair.

Answer 2

- Kala should definitely not doubt whether the die is a fair die. The two probabilities are relatively close so the die is most likely to be fair.

Answer 3

- Kala should definitely doubt whether the die is a fair since the experimental probability of rolling that many 6s is much greater than the binomial probability of doing so.

Answer 4

THOSE ARE THE OPTIONS LISTED ABOVE ^^^

Answer 5

are you familiar with the binomial probability distribution?

Answer 6

not quite.

Answer 7

this formula doesn't look familiar?

\[\Large \left(_n C _k\right)*\left(p\right)^{k}*\left(1-p\right)^{n-k}\]

Answer 8

If you want, you can use this calculator instead

http://stattrek.com/online-calculator/binomial.aspx

Answer 9

oh yes I've definitely seen it before but am a little confused on how to apply it to an equation

Answer 10

So you've dealt with permutations and combinations before?

Answer 11

I don't think I've ever heard of those terms ever...but for some reason the formula you sent me looks quite familiar

Answer 12

So you've seen this formula before?

\[\Large _n C _r = \frac{n!}{r!*(n-r)!}\]

or no?

Answer 13

no never

Answer 14

ok then it will probably be best to stick with the calculator I posted above

Answer 15

ok so how do I apply the calculator to the question I'm asking..?

Answer 16

there are 6 sides on a die. The probability of landing on any one side is 1/6 = 0.1667

we're doing 10 trials

we want x to be equal to 5

Answer 17

so you'll type 0.1667 into the first box
10 in the second box
5 in the third box

then hit "calculate"

Answer 18

what value pops up next to `Binomial Probability: P(X = 5) ` ?

Answer 19

.0130

Answer 20

so that is the answer to
`The binomial probability of rolling five 6s out of ten throws is approximately _____. `

Answer 21

`The experimental probability of rolling a 6 is _____.`

five 6's are rolled out of 10 trials, so 5/10 = 0.5 is the answer for this part

Answer 22

question: is the die fair? why or why not?

Answer 23

am I supposed to answer that question?

Answer 24

it asks `Should Kala doubt whether the die is a fair die?`

Answer 25

would the first option be correct?

Answer 26

what do you mean by "first option"?

Answer 27

Kala might doubt whether the die is a fair die, since the experimental probability of rolling that many 6s is much greater than the binomial probability. However, since there were only 10 experiments, the die still may be fair.

Answer 28

I'm guessing there are other options? What are they?

Answer 29

I listed them on the top. can u not see them? if not I can easily copy/paste them again

Answer 30

oh right, brainfart

ok one sec

Answer 31

I would go with
`- Kala should definitely doubt whether the die is a fair since the experimental probability of rolling that many 6s is much greater than the binomial probability of doing so.`
because the die seems to be unfair. It seems like there is more than one face with '6' on it. Or the face opposite '6' is weighed down to make 6 come up more frequently

Answer 32

ok I was gonna say it was either gonna be she might doubt or just all together doubt the fact that the die isn't fair

Answer 33

Thank you again for your help!

Answer 34

That's a good point. 10 trials may not be enough. Still, I think it is rigged in favor of '6'

Answer 35

Also on this question I just wanted to make sure I got the right answer. I'm pretty sure it's the correct one so if you could please take a second to check, that would be amazing

Answer 36

Which of the equations of hyperbolas below has a vertical asymptote at x = -3?

Answer 37

y=6/(x-4) -3

Answer 38

@jim_thompson5910

Answer 39

you only listed one equation

Answer 40

oh it was either that one or this one

Answer 41

y=4/(x-3) +6

Answer 42

so only two options?

Answer 43

yes

Answer 44

none of the answer choices are the answer. You need a `x+3` in the denominator to have a vertical asymptote of x = -3

Answer 45

oh that was my bad! the plus was supposed to be a minus!

Answer 46

so instead of `y=4/(x-3) +6` it's actually `y=4/(x+3) +6` ?