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15 February, 01:49

Acercal 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. Each dot represents how many boxes it took to get all 4 prizes in

that trial.

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  1. 15 February, 01:56
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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 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.
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