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.
$$
P(9 \text { or more boxes }) \approx
$$
$\square$

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. 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.
$$
P(9 \text { or more boxes }) \approx
$$
$\square$

Accepted Answer

∻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: $$ P(9 ext{ or more boxes}) = \frac{4}{32} = \frac{1}{8} = 0.125 $$ ‖ ∻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.⚹◊What is the expected value of the number of boxes Adam needs to purchase to get all 3 prizes based on the results of 32 trials?⍭ Generate me a similar question◊

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