Acercal company is putting of 4 prizes in each box of cereal. The prizes are evenly distributed so the

probability of winning any given prize is always 1/4.

Lily wonders how many boxes she should expect to buy to get all 4 prizes. She carried out 20 trials of a

simulation and her results are shown below. Each dot represents how many boxes it took to get all 4 prizes in

that trial.

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

A cereal company is putting of 4 prizes in each box of cereal. The prizes are evenly distributed so the probability of winning any given prize is always 1/4.

Lily wonders how many boxes she should expect to buy to get all 4 prizes. She carried out 20 trials of a simulation and her results are shown below.

No. of Boxes | frequency

4 | 6

5 | 2

6 | 2

7 | 0

8 | 3

9 | 2

10 | 2

11 | 1

12 | 2

Use his results to estimate the probability that it takes 9 or more boxes to get all 4 prizes. Give your answer as either a fraction or a decimal.

P (9 or more boxes) =

Answer:

P (x ≥ 9) = 0.35

Step-by-step explanation:

We are given that a cereal company is putting of 4 prizes in each box of cereal.

The probability of winning any given prize is always 1/4.

Lilly is wondering how many boxes she should buy to get all 4 prizes so she carried out 20 trials.

We want to estimate the probability that it takes 9 or more boxes to get all 4 prizes.

Let x be the required number of boxes then the required probability is given by

P (x ≥ 9) = No. of times boxes equal or greater than 9/total no. of boxes

Total no. of boxes = 20

From the given simulation results count the number of times she got boxes equal to 9 or greater than 9.

No. of times boxes equal or greater than 9 = 2 + 2 + 1 + 2 = 7

P (x ≥ 9) = 7/20

P (x ≥ 9) = 0.35

P (x ≥ 9) = 35%

Therefore, there is 35% probability that it takes 9 or more boxes to get all 4 prizes.