what is the probability of one persons tie being too tight

Question

25% of buisness men where ties too tight. At a board meeting of 20 men all of whom wore ties.

Answer 1

Hi Susanne

 

There is another way to look at this.  You could use the formula for binomial probabilities

to solve for the probabilty that one persons tie is too tight

 

the formula uses factorials and probabilities

 

_n C _r  * p^r * q^n-r

 

where n is the number of possibilities

r is the number of times you the event will happen (in our case r = 1 the number of ties being too tight)

 

p = probability that a tie is too tight

q = probability that is not too tight

 

so we would have the following

 

p = .25

q = .75

 

n = 20

r = 1

 

_n C _r  = 10

 

p¹ = .25

 

q¹⁹ = .004228

 

multiply these all together and we get the probability of just one tie being too tight

 

and this equals .010571  or about 1.06%

 

 

 

Answer 2

Susanne,

 

The answer they are looking for is  p = 0.25, the decimal version of 25%.  BTW, divide % by 100 to convert to decimal, and multiply by 100 to go from decimal to %.

 

But in another sense, the probability is unknown from the data supplied. The data is for a sample of 20 corporate or institutional board members.  How representative are such people of men in the general population?  For example, board members are probably older, may not be into the latest fashions, may use knots that give a tighter tie, etc.