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

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.

andromache andromache · Answer 2 · 2022-01-29T05:01:01+01:00

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

The calculation is as follows:

No. of Boxes | frequency

3 | 12

4 | 4

5 | 5

6 | 5

7 | 0

8 | 0

9 | 2

10 | 2

11 | 0

12 | 2

Here 9 or more boxes represent that it is equal to 9 boxes or more than 9 boxes.

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

And, The total no. of boxes is 32

From the above data, we have to count the number of boxes equal to or more than 9. (6 times) i.e.

[tex]P(x $\geq$ 9) = 6\div 32\\\\P(x $\leq$ 9) = 3\div 16[/tex]

P(x ≥ 9) = 0.1875

P(x ≥ 9) = 18.75%

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