Find the probability of “x” successes given the probability of “P” success on a given trial.

Question

A) n=3 x=0 P=0.05

B)n=4 X=3 P=.30

C)n=5 x=2 P=.25

Answer 1

n=3, P = .05, x=0

zero successes on 3 tries with 5% chance of success on each is: (.95)^3 = .857375= 85.7%

(1-.05)^3 = .857375, = .857 rounded off to 3 decimal places

there's only one way to get zero successes in 3 tries

FFF (F for failure, S for Success)

multiply the probability of failure times the probability of failure times the probability of failure=(.95)^3

n=4, x=3, P=.30

3 successes on 4 tries with 30% chance of success: .3(.3)(.3)(.7)(.7)4= 0.05292= 5.3%

(.3)(.3)(3)(1-.3)(1-.3)(4) = 0.05292

multiply the probability of success times probability of success times probability of success times probability of failure times probability of failure = (.3)^3(.7)^2 = .01323 then multiply that by 4 to get 0.5292

there are 4 ways to get 3 successes in 4 tries

SSSF

SSFS

SFSS

SSFF

n=5, x=2, P=.25

2 successes in 5 tries with 25% chance of success: (.25)(.25)(.75)(.75)(.75)10 = .263671875= about 26.4%

(.25)(.25)(1-.25)(1-.25)(1-.25) = 0.026367187

multiply by 10

there's 10 ways to get 2 successes and 3 failures

SSFFF

SFSFF

SFFSF

SFFFS

FSSFF

FSFSF

FSFFS

FFSSF

FFSFS

FFFSS