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

Answer:

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 )

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

               = $\frac{6!}{(2!)(4!)}(.23)^{2}(.77)^{6 - 2}$

              =   $\frac{6!}{(2!)(4!)}(.23)^{2}(.77)^{4}$

              =  $15\times.0529\times.3515$

              = .2789