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

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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 ) =

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.