Suppose a cereal company puts one of six possible prizes in each cereal box. You

can use a simulation involving rolling a six-sided die to determine the probability

distribution for getting a particular prize in four purchased boxes of cereal.293/nel

Define a success as the appearance of a 1. What is the probability for one,

two, three, four, or zero 1s showing?

construct a simulation of this experiment using a spreadsheet for 100 repetitions of the simulation

• construct a histogram showing no. of 1's and experimental probability.
• Verify that the die-roll simulation is a binomial experiment by checking that it
• Use the simulation to answer the following questions

has all the required properties of a binomial distribution.

(a) What is the probability that the first roll will be a 1 and all the others will be

something other than a 1?

(b) Find the probability of the combined event that the roll of 1 will appear in

any of the four available positions in the table.

(c) What is the probability that exactly two 1s show in the four rolls of the die?

(d) Complete the theoretical probability distribution for the number of 1s

showing in four rolls

(e) Find the expected value of this experiment.