Suppose 73% of people like carrots.In a sample of 6 people ,What is the probability that at least 5 of them like carrots?
+6251 \(\mbox{This problem is an example of a binomial distribution. here }n=6, p=0.73 \\ \\ \\ P[\mbox{k of 6 like carrots}]=\begin{pmatrix}n \\ k \end{pmatrix}p^k (1-p)^{n-k} \\ \\ \\ \mbox{The probability that at least 5 like carrots is }P[5]+P[6] = \\ \\ \\ \begin{pmatrix}6 \\ 5\end{pmatrix}(0.73)^5(0.27)^1 + \begin{pmatrix}6 \\ 6\end{pmatrix}(0.73)^6(0.27)^0 = \\ \\ \\ (6)(0.2073)(0.27) + (1)(0.1513)(1) = 0.487126\)
.+6251 \(\mbox{This problem is an example of a binomial distribution. here }n=6, p=0.73 \\ \\ \\ P[\mbox{k of 6 like carrots}]=\begin{pmatrix}n \\ k \end{pmatrix}p^k (1-p)^{n-k} \\ \\ \\ \mbox{The probability that at least 5 like carrots is }P[5]+P[6] = \\ \\ \\ \begin{pmatrix}6 \\ 5\end{pmatrix}(0.73)^5(0.27)^1 + \begin{pmatrix}6 \\ 6\end{pmatrix}(0.73)^6(0.27)^0 = \\ \\ \\ (6)(0.2073)(0.27) + (1)(0.1513)(1) = 0.487126\)
