Question

Statistics

Posted 5 months ago

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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. Each dot represents how many boxes it took to get all 3 prizes in that trial.
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.
$P(9 \text { or more boxes }) \approx$
$\square$
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Answer from Sia

Posted 5 months ago

Solution by Steps

step 1

First, we need to count the number of trials where it took 9 or more boxes to get all 3 prizes. From the given data:
- 9 boxes: 1 dot
- 10 boxes: 1 dot
- 11 boxes: 1 dot
- 13 boxes: 1 dot
So, there are a total of $1 + 1 + 1 + 1 = 4$ trials where it took 9 or more boxes

step 2

Next, we calculate the total number of trials, which is given as 32

step 3

To find the probability, we divide the number of trials where it took 9 or more boxes by the total number of trials:
$P(9 \text{ or more boxes}) = \frac{4}{32} = \frac{1}{8} = 0.125$

Answer

$0.125$

Key Concept

Probability estimation from a dot plot

Explanation

The probability is estimated by dividing the number of favorable outcomes (trials with 9 or more boxes) by the total number of trials.

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