Question

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?

Answer 1

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

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 )

`P(X = r )= \binom{n}{r}(p)^(r)(q)^(n - r)`

=
`(6!)/((2!)(4!))(.23)^(2)(.77)^(6 - 2)`

=
`(6!)/((2!)(4!))(.23)^(2)(.77)^(4)`

=
`15*.0529*.3515`

= .2789