A soda manufacturer knows that sales of soda increase during the summer. To make sure that they get a large portion of the sales, they decide to offer a contest throughout the spring. The contest is pretty simple: when you open your bottle of soda, if it says, “You win!” under the cap, you get another bottle of their soda for free. The chance of winning a free soda is 1 in 12. Lucky Lucy bought five sodas and won a free one with four of the caps. What’s the probability of that happening? Theoretically, how many sodas would you have to buy before having a greater than 50% chance of winning a free soda?

a.) Probability = 1/5

b.) 10 soda

Step-by-step explanation:

Probability is a game of chance.

The initial chance = 1/12

If Lucky Lucy bought five sodas and won a free one with four of the caps. The probability of that happening will be 1/5

Having a greater than 50% chance of winning a free soda means having probability greater than half. That is,

Probability > 1/2

You would have to buy (12 - 2) soda. Which is equal to 10.

the image is given below

since the options are not given so we draw it from the equation

the given equation is

y = (x-1) (x+4)

y = y² + 3x - 4

the above equation is a quadratic equation which will have two roots. if we draw the graph for it, it will look like this