Answer:A) 0.9866
Step-by-step explanation:
Probability of at least one tie is too tight is
Probability of tight tie 25/100
Probability of not a tight tie is 1-25/100=3/4
=1-(3/4)^15=0.9866
B)0.764
C)0.013
D)0.236
Method 2
This is binomial probability.
n=15 (number of businessmen
p=.25 (probability that a businessman wears the tie so tightly
A)
x = number of businessmen out of 15 who wears the tie so tightly
P( at least 1) = P( x >= 1) = 1-P(x=0)
P(x=0) = 15C0 (.25)^0 (.75)^(15-0) = (0.75)^15 = 0.013363
P( at least 1) = 1- 0.013363 = 0.9866
B)
P(more than 2) = P( x > 2) = 1-P( x=0)-P(x=1)-P(x=2)
P(x=0) = 15C0 (.25)^0 (.75)^(15-0) = (0.75)^15 = 0.013363
P(x=1) = 15C1 (.25)^1 (.75)^14 = 0.066817
P(x=2) = 15C2 (.25)^2 (.75)^13 = 0.155907
1-P( x=0)-P(x=1)-P(x=2) = 1 - 0.013363 - 0.066817 - 0.155907 = 0.763912
C)
P(x=0) = 15C0 (.25)^0 (.75)^(15-0) = (0.75)^15 = 0.013363
D)
P( at least 13) = P(x=13)+P(x=14)+P(x=15)
P(x=13)= 15C13 (.25)^13 (.75)^2 = 0.000001
P(x=14)= 15C14 (.25)^14 (.75)^1 = 0.000000
P(x=15)= 15C15 (.25)^15 (.75)^0 = 0.000000
P(x=13)+P(x=14)+P(x=15) = .000001+.000000+.000000 = 0.000001
