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# Republished: BINOMIAL PROBABILITY

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Hello!
Can someone help me understand how to go about answering these questions for binomial distributions?

n=8, p=0.2

Find P(X=3)

Find P(X≤3)

Find P(X>4)

Find P(X<5)

Find P(X≥3)

Find P(3

I know these are alot of questions but I missed this lesson because of an illness and have a test to write tomorrow and have zero information on how to answer/do them.

Any help would be very much appreciated! Thank you!

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#1
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Not an expert on these....but I believe that we have :

8  = number of trials    p = probability of success on any trial = .2

probability of failure on one trial  = 1 - .2  = .8

P(3)  = means "probability of  3 successes in 8  trials "  =

C(8,3) (.2)^3 (1 - .2)^(8-3)  = C(8,3) (.2)^3 (.8)^5  ≈  14.68%

P (≤3 ) = means probability of  0 successes in 8 trials + probability of  1 success in 8  trials + probability of  2 successes in 8  trials + probability of  3 success in 8  trials  =

C (8,0) (.2)^0 (.8)^8  +  C (8,1) (.2)^1 (.8)^7 + C (8,2) (.2)^2 (.8)^6 + C (8,3) (.2)^3 (.8)^5  ≈

94.37%

P ( > 4) =

C (8,5) (.2)^5 (.8)^3  +  C (8,6) (.2)^6 (.8)^2 + C (8,7) (.2)^7 (.8)^1 + C (8,8) (.2)^8 (.8)^0  ≈

1.04%

Based on this....Can you do the rest ???...if not....let me know....

Note also  :  P(> 4)  = 1 - P( ≤ 4 )

CPhill  Oct 29, 2017
#2
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Yes! This helped loads! I seem to get it now.