Question

You roll a red number cube and a blue number cube. Let A be the event "at least one number cube shows a 6"

a) Find P(A) by finding the sum of P(6 on red cube, no 6 on blue cube), P(no 6 on red cube, 6 on blue cube), and P(6 on both cubes)

b) Describe the event "not A" then find P(not A) and use it to find P(A)

c) Compare the methods in part a and b.

Answer 1

Assuming both are fair cubes.
Any fair cube will give a "6" with theoretical probability of 1/6.
(a)
For case
Red cube: P(6)=1/6, P(~6)=5/6
Blue cube: P(6)=1/6, P(~6)=5/6
Using the multiplication rule for the two step experiment (red, then blue),
P(6R,~6B)=1/6*5/6
P(~6R,6B)=5/6*1/6
P(6R,6B)=1/6*1/6
Add the sum of probabilities of the three cases above.

(b) ~A=both cubes don't show a 6.
P(~A)=5/6*5/6
P(A)=1-P(~A)= ?
(c)
Do your comparison.

In probability, it is advantageous to work with fractions whenever possible because it will give unambiguous results.

Answer 2

I have no idea what the answer could possibly be