A cereal company is putting 111 of 444 prizes in each box of cereal. The prizes are evenly distributed so the probability of winning any given prize is always 1/41/41, slash, 4. Vera wonders how many boxes she should expect to buy to get all 444 prizes. She carried out 363636 trials of a simulation and her results are shown below. Each dot represents how many boxes it took to get all 444 prizes in that trial.

(27/36) = (3/4) = 0.75

Step-by-step explanation:

The complete question is attached to this solution.

P(9 or fewer boxes) = P(x ≤ 9)

Since Vera carried out the simulation/experiment, this probability will be read from the results of her simulation (the dotplot).

Note that the dots on the numbers of the dotplot represent the number of boxes it took Vera to get all the prizes.

So, the probability of getting all the prizes in 9 or fewer boxes will be just counting the number of times in the simulation where she got the 4 prizes in 9 boxes or fewer.

This starts from the least number on the dotplot, 4 all the way to 9.

Total number of simulations = 36

P(x ≤ 9) = P(x=4) + P(x=5) + P(x=6) + P(x=7) + P(x=8) + P(x=9)

= (4/36) + (6/36) + (3/36) + (4/36) + (4/36) + (6/36) = (27/36)

Hope this Helps