A cereal company is putting 111 of 333 prizes in each box of cereal. The prizes are evenly distributed so the probability of winning any given prize is always 1/31/31, slash, 3. Adam wonders how many boxes he should expect to buy to get all 333 prizes. He carried out 323232 trials of a simulation and his results are shown below. Each dot represents how many boxes it took to get all 333 prizes in that trial.
A dot plot for number of boxes purchased has a scale from 3 to 13. The number of dots for each is as follows. 3, 8. 4, 7. 5, 5. 6, 3. 7, 3. 8, 2. 9, 1. 10, 1. 11, 1. 12, 0. 13, 1.
Use his results to estimate the probability that it takes 999 or more boxes to get all 333 prizes.
Give your answer as either a fraction or a decimal.
P(9 \text{ or more boxes})\approxP(9 or more boxes)≈P, left parenthesis, 9, start text, space, o, r, space, m, o, r, e, space, b, o, x, e, s, end text, right parenthesis, approximately equals