Respuesta :
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.
