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 or more boxes) ≈

Explanation:

Step1: Count the number of favorable outcomes

Count the number of dots for \(9\), \(10\), \(11\), \(12\), and \(13\) boxes.
For \(9\) boxes: \(1\) dot.
For \(10\) boxes: \(1\) dot.
For \(11\) boxes: \(1\) dot.
For \(12\) boxes: \(0\) dots.
For \(13\) boxes: \(1\) dot.
Total favorable outcomes \(=1 + 1+1+0 + 1=4\).

Step2: Count the total number of trials

The total number of trials \(n = 32\).

Step3: Calculate the probability

The probability formula is \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\).
So \(P=\frac{4}{32}=\frac{1}{8}=0.125\).

Answer:

\(0.125\)