A cereal company is putting 1 11 of 3 33 prizes in each box of cereal. The prizes are evenly distributed so the probability of winning any given prize is always 1 / 3 1/31, slash, 3. Adam wonders how many boxes he should expect to buy to get all 3 33 prizes. He carried out 32 3232 trials of a simulation and his results are shown below. Each dot represents how many boxes it took to get all 3 33 prizes in that trial. 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13# of boxes purchased Use his results to estimate the probability that it takes 9 99 or more boxes to get all 3 33 prizes. Give your answer as either a fraction or a decimal. P (9 or more boxes) ≈ P (9 or more boxes) ≈P, left parenthesis, 9, start text, space, o, r, space, m, o, r, e, space, b, o, x, e, s, end text, right parenthesis, approximately equals

0.125

Explanation:

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

Question:

A cereal company is putting 1 of 3 prizes in each box of cereal. The prizes are evenly distributed so the probability of winning any given prize is always 1/3. Adam wonders how many boxes he should expect to buy to get all 3 prizes. He carried out 32 trials of a simulation and his results are shown below.

3 12

4 4

5 5

6 5

7 0

8 0

9 2

10 2

11 0

12 2

Use his results to estimate the probability that it takes 9 or more boxes to get all 3 prizes. Give your answer as either a fraction or a decimal. P (9 or more boxes) =

Answer:

P (x ≥ 9) = 18.75%

Step-by-step explanation:

A cereal company is putting 1 of 3 prizes in each box of cereal.

Adam is trying to find out how many boxes he should buy to get all 3 prizes.

He carried out 32 trials and got the following results.

We want to estimate the probability that it takes 9 or more boxes to get all 3 prizes.

No. of Boxes | frequency

3 | 12

4 | 4

5 | 5

6 | 5

7 | 0

8 | 0

9 | 2

10 | 2

11 | 0

12 | 2

9 or more boxes means equal to 9 boxes or greater than 9 boxes.

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

The total no. of boxes is 32

From the above data, count the number of boxes equal to or greater than 9. (6 times)

P (x ≥ 9) = 6/32

P (x ≥ 9) = 3/16

P (x ≥ 9) = 0.1875

P (x ≥ 9) = 18.75%

Therefore, there is 18.75% probability that it takes 9 or more boxes to get all 3 prizes.