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Binomial Distribution question (quick)

could someone help me do this question pls?

1) Number of successes in N independant trials is X. Probability of success in each trial is P

Given that n=10, p = 1/4, find P(X=3)


:eek:
Reply 1
Avatar for Peevee
Peevee
magnum
Given that n=10, p = 1/4, find P(X=3)


X~B(10,0.25)

P(X=3) = 10C3.(0.25)³.(0.75)^7 = 0.25 (2.d.p)
Reply 2
Avatar for magnum
magnum
OP
4
thanks mate!
Reply 3
Avatar for Peevee
Peevee
No probz :cool:
Reply 4
Avatar for magnum
magnum
OP
4
Peevee
X~B(10,0.25)

P(X=3) = 10C3.(0.25)³.(0.75)^7 = 0.25 (2.d.p)



so how did you get the 0.25 as the answer?
Reply 5
Avatar for steve2005
steve2005
17
magnum
so how did you get the 0.25 as the answer?

Here is the method using factorials
Picture 19.png25.0KB
Reply 6
Avatar for magnum
magnum
OP
4
oh yea, i get that now.

but if n=7 p=0.5 , find P(less than or equal to 3 less than or equal to 5)

how would i do P?
Reply 7
Avatar for Peevee
Peevee
magnum
oh yea, i get that now.

but if n=7 p=0.5 , find P(less than or equal to 3 less than or equal to 5)

how would i do P?


X~B(7, 0.5)

P(X « 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

P(X = 0) = 7C0.(0.5)^0.(0.5)^7 = (7.8125 x 10^-3)
P(X = 1) = 7C1.(0.5)^1.(0.5)^6 = 0.0546875
P(X = 2) = 7C2.(0.5)^2.(0.5)^5 = 0.1640625
P(X = 3) = 7C3.(0.5)^3.(0.5)^4 = 0.2734375

P(X « 3) = (7.8125 x 10^-3) + 0.0546875 + 0.1640625 + 0.2734375 = 0.5

NB, don't round numbers until the very end. :smile:
Reply 8
Avatar for magnum
magnum
OP
4
wooooooooowza

thanks once again o kind sir :biggrin:
Reply 9
Avatar for magnum
magnum
OP
4
btw, have you just done the (x is less than or equal to 3)?

because the question i have is («3 X «5)
I hate calculators :smile:
magnum
oh yea, i get that now.

but if n=7 p=0.5 , find P(less than or equal to 3 less than or equal to 5)

how would i do P?


Here is a bit of the solution. The rest I leave to u.
Picture 20.png16.6KB
Reply 12
Avatar for magnum
magnum
OP
4
steve, the bit i want to know is do i do (x=«3) + (x=«5)?
Reply 13
Avatar for Peevee
Peevee
magnum
steve, the bit i want to know is do i do (x=«3) + (x=«5)?


Do you mean ...(X « 3) and (X » 5) ?
Reply 14
Avatar for magnum
magnum
OP
4
Peevee
Do you mean ...(X « 3) and (X » 5) ?


its ok, ive done that now :biggrin:

thanks everyone.
magnum
steve, the bit i want to know is do i do (x=«3) + (x=«5)?


I have done this quickly..... it might be wrong.

Something is wrong .... I'm rushing. See Excel sheet pic 22

Pic 22 is wrong. Pic 23 is correct.
Picture 21.png42.3KB
Picture 22.png7.8KB
Picture 23.png8.3KB

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