A survey on British Social Attitudes asked respondents if they had ever boycotted goods for ethical reasons (Statesman, January 28, 2008). The survey found that 23% of the respondents have boycotted goods for ethical reasons.

In a sample of six British citizens, what is the probability that two have ever boycotted goods for ethical reasons?

The probability that two have ever boycotted goods for ethical reasons.= .2789

Step-by-step explanation:

Given - The survey found that 23% of the respondents have boycotted goods for ethical reasons .

The probability of success ( p) = 23 = 0.23

The probability of failure ( q) = 1 - p = .77

n = 6  

Let X be the number of British citizens boycotted goods for ethical reasons.

The probability that two have ever boycotted goods for ethical reasons.

( Using Binomial distribution )

               =

              =  

              =  

              = .2789

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4