Suppose we watch the price of the Dow Jones Industrial Index for three days.

Assume there is a 60:40 chance that the price will either go up or down.

Let A: Event that there are an odd number of up days

Let B: Event that there are at least 2 up days

Let C: Event that there are exactly 3 down days

Let D: Event that there at most 2 down days

Let E: Event that there are at most 1 up day

a) Write down the sample space for this experiment.

b) Find the probabilities of the above mentioned events.