Answer:
The probability that you win something is 0.7916.
Step-by-step explanation:
Let <em>X</em> denote the number of soda bottles having winning symbols under the caps.
The proportion of soda bottles having winning symbols under the caps is, <em>p</em> = 0.23.
Six-pack of soda are randomly bought.
Every bottle is independent of the others to have the symbols under the caps.
The random variable <em>X</em> follows a binomial distribution with parameters <em>n</em> = 6 and <em>p</em> = 0.23.
Then the chance of winning something implies that at least 1 of the bottles in the six-pack have the symbol under the caps.
Compute the value of P (X ≥ 1) as follows:
![P(X\geq 1)=1-P(X](https://tex.z-dn.net/?f=P%28X%5Cgeq%201%29%3D1-P%28X%3C1%29%5C%5C%5C%5C%3D1-P%28X%3D0%29%5C%5C%5C%5C%3D1-%7B6%5Cchoose%200%7D%280.23%29%5E%7B0%7D%281-0.23%29%5E%7B6-0%7D%5C%5C%5C%5C%3D1-0.2084224%5C%5C%5C%5C%3D0.7915776%5C%5C%5C%5C%5Capprox%200.7916)
Thus, the probability that you win something is 0.7916.