Question

Get rid of the penny Harris Interactive reported that 29% of all U.S. adults favor abolishing the penny. Assuming that responses from different individuals are independent, what is the probability of randomly selecting 3 U.S. adults who all say that they favor abolishing the penny?

Short answer

The required probability is$0.0244$

Step-by-step solution

Given information

Given that,

Probability of success $\left(p\right)=29\%=0.29$

Number of trials$\left(n\right)=3$

Calculation

The probability of a binomial distribution can be calculated using the following formula:

$P(X=r)={}^{n}C_r\times p^r\times (1-p{)}^{n-r}\mathrm{P}$

The probability of selecting adults who are in favor of abolishing the penny at random is calculated as follows:

$P(X=r)={}^{n}C_r\times p^r\times {(1-p)}^r={}^{3}C_3\times {(0.29)}^3\times {(1-0.29)}^{3-3}=0.0244$

Therefore, the required probability is$0.0244$