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}](https://tex.z-dn.net/?f=P%28X%20%3D%20r%20%29%3D%20%5Cbinom%7Bn%7D%7Br%7D%28p%29%5E%7Br%7D%28q%29%5E%7Bn%20-%20r%7D)
= ![\frac{6!}{(2!)(4!)}(.23)^{2}(.77)^{6 - 2}](https://tex.z-dn.net/?f=%5Cfrac%7B6%21%7D%7B%282%21%29%284%21%29%7D%28.23%29%5E%7B2%7D%28.77%29%5E%7B6%20-%202%7D)
= ![\frac{6!}{(2!)(4!)}(.23)^{2}(.77)^{4}](https://tex.z-dn.net/?f=%5Cfrac%7B6%21%7D%7B%282%21%29%284%21%29%7D%28.23%29%5E%7B2%7D%28.77%29%5E%7B4%7D)
= ![15\times.0529\times.3515](https://tex.z-dn.net/?f=15%5Ctimes.0529%5Ctimes.3515)
= .2789