Consider a binomial random variable with n = 9 and p = 0.3. Let x be the number of successes in the sample.
a. Find the probability that x is exactly 2.
b. Find the probability that x is less than 2.
c. Find P(x > 2).
d. Find P(2 ≤ x ≤ 4).
I've solved the a) but I can't get the other 3. I got 0.267 for a).

- anonymous

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- anonymous

For B, note that P(x < 2) = P(x = 0) + P(x = 1) since these are the only two values the random variable can take below 2.

- anonymous

So do i have to do the same thing i did for part a but repeat it for x = 0 and x = 1?

- anonymous

Yep, since you know how to calculate the probability the variable is equal to something you can use that to find the probability it is less than something.

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- anonymous

okay and for part c i do tht for x = 3 all the way up to 9? that would take forever...

- anonymous

For part C you can use the fact that P(x > 2) + P(x <= 2) = 1 and use your previous answers to calculate P(x > 2).

- anonymous

Otherwise you're right, it is a bunch of boring calculation :P

- anonymous

I dont understand

- anonymous

If something is not larger than 2, then that means it's less than or equal to 2. So P(x > 2) = 1 - P(x <= 2). From your first two answers you can calculate P(x <= 2) easily so that's why we do it this way.

- anonymous

Im sorry I still dont get it

- anonymous

That's ok, I'm just trying to think of ways to explain it :P Do you know that if you know the probability of something happening then the probability of it not happening is 1 minus that probability?

- anonymous

yeah

- anonymous

btw i think i solved part b is it 0.196?

- anonymous

It is :) So do you agree that P(x > 2) = 1 - P(x <= 2)?

- anonymous

I dont understand that formula

- anonymous

It comes from what I said above combined with the fact that is x is not > 2, then it is <= 2.

- anonymous

okay that makes sense

- anonymous

Alright. So can you find P(x <= 2)?

- anonymous

i did c9,1(0.3)^2(0.7)^9-1 and the same this for 0 to get 0.196

- anonymous

i used an online calculator to solve it because i dont know how to do it on my calclator

- anonymous

0.196 is P(x < 2), but you need P(x <= 2)

- anonymous

no part b says just less than 2
and i found out how to do it on my calculator had to use the nCr key

- anonymous

I mean for part C, since we know that P(x > 2) = 1 - P(x <= 2)

- anonymous

so would P(x <=2) be 0.267 + 0.196?

- anonymous

Yes. Then you can find the answer to C

- anonymous

so c would be 1 - (0.267+0.196)?

- anonymous

Yep!

- anonymous

Wow! thank you I actually understand what you were trying to say earlier

- anonymous

okay so how would i go about doing part d?

- anonymous

is it asking to find x = 3?

- anonymous

Well if 2 <= x <= 4 then that means x can be 2, 3, or 4.

- anonymous

right so how can i approach this?

- anonymous

would i have to solve for x = 2,3,4?

- anonymous

Yeah, I think the easiest way to do it here is to just calculate the probabilities for each case and sum them.

- anonymous

:( okay well atleast I know how to do these srot of questions thank you so much JE!

- anonymous

No worries, glad I could help! :)

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