Question

Probability question

Answer 1

How many times must you roll a four sided die so that the probability of getting at least 3 twos is 0.3214?

Answer 2

You have studied bernoulli trials.

Answer 3

@samigupta8 Is that similar to binomial theorum?

Answer 4

Yeah!

Answer 5

In this , we have n trials out of which we represent p- success and q-failure.
Then we write accordingly

Answer 6

Ohh, cool @samigupta8
What would p and q be in this case though, the probability of getting a 2 and not gettinga 2?

Answer 7

I am impressed!

Answer 8

@samigupta8 but then how do we solve if we don't know n?

Answer 9

We can !

Answer 10

How? o:

Answer 11

Can you write the numerical representation of the problem?
With the help of info,i gave you.

Answer 12

\[p(n)=C(n,r) \times (1/6)^r \times (5/6)^{n-r}\]

Answer 13

Is that it?

Answer 14

Don't you think that it should be (5/6)^r and (1/6)^(n-r)?

Answer 15

Aren't we looking for at least 3 times its 2, so we use r as the number of times we get 2, a chance of 1/6? I think im not understanding something :(

Answer 16

First of all, i should tell you that we start by writing it as
nCr (p)^(n-r) (q)^r

Answer 17

r is the number of times we need to get the desired result.

Answer 18

Yup :)
is p = 1/6?

Answer 19

Yo

Answer 20

Four sided dice is not a six sided dice.
Isn't it?

Answer 21

OHHHHH YEAH
So r=1/4?

Answer 22

No

Answer 23

It's the value of p

Answer 24

And i told you what is r.

Answer 25

@ahsome are you getting it?

Answer 26

SORRY, i was tryign to do it myself.

So p = 1/4 right?

Answer 27

Yeah.

Answer 28

But how do you know r?

Answer 29

It's given that at least 3 times.
So we have to do it like subtract the probability of 0,1, and 2 success from 1

Answer 30

You here!

Answer 31

OHH, I see. Doesm't that just give you the probability, and not the amount needed? Don't they give aprobability of 0.3124?

Answer 32

Yeah! That's how you can get value for n .

Answer 33

Ohh, OK
So we know that p=1/4, q = 3/4, r = 0, 1, and 2. Now we just find n?

Answer 34

Yeah.

Answer 35

How do we find n?

Answer 36

1- all the probability upto no. of success 2 .

Answer 37

Would return after about 3 hours. A bit sleepy. Sorry!

Answer 38

OK then :) See ya @samigupta8
I am not sure the equation to find n, but ill try to do it