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.
