Question

A cereal company is giving away 1 of 6 different prizes in each box of cereal. Describe a simulation you could use to estimate the number of boxes needed to get all 6 prizes.
I’ll give brainliest but i need to turn in it in like half an hour

Answer 1

Answer:

The appropriate simulation is a fair dice with each side representing one of the prizes

Step-by-step explanation:

Here we have a simulation with a fair dice

A fair dice is a cube with each of the six faces having a value of 1 to 6 and the probability of any face turning up is the same for all faces 1/6. That is all the chance that a 1 shows face up is 1/6 similarly, the probability that a 4 shows face up is 1/6.

Therefore, in the simulation, each face of the fair dice represent one of the prizes therefore the number of times the dice is thrown to get all six numbers is the number of boxes you need to get all the prize

At its simplest, a fair dice means that each of the faces has the same probability of landing facing up. A standard six-sided dice, for example, can be considered "fair" if each of the faces has a probability of 1/6.

Therefore to have all the prizes you need at least

$\frac{6}{6}\times \frac{5}{6}\times \frac{4}{6}\times \frac{3}{6}\times \frac{2}{6}\times \frac{1}{6} = \frac{5}{324}$

or the chance of getting all the prices is 0.01543 or once in 1620 trials

That is 1620 boxes are needed to be sure of getting all 6 prizes.