For a sales promotion, the manufacturer places winning symbols under the caps of 27 % of all its soda bottles. If you buy a six-pack of soda, what is the probability that you win something?

84.87% probability that you win something

Step-by-step explanation:

For each bottle of soda, there are only two possible outcomes. Either there is a winning symbol, or there is not. For each bottle, the probability of having a winning symbol is independent from other bottles. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

In this problem we have that:

If you buy a six-pack of soda, what is the probability that you win something?

You will will something if at least one of the bottles has a prize.

We know that either no bottles have a prize, or at least one does. So

We want . So

In which

84.87% probability that you win something

0.849

Step-by-step explanation:

P(winning something)

= 1 - P(winning nothing)

= 1 - (1-0.27)⁶

= 1 - 0.73⁶

= 0.8486657737