You have three jazz CDs denoted c1 c2 c3 The first two c1 an

You have three jazz CDs, denoted c_1, c_2, c_3. The first two (c_1 and c_2) can be read and played properly by your CD player, but c_3 is scratched and cannot be read properly. You randomly select two different CDs. one at a time, to play. Let the outcome be the ordered pair of CDs selected. Let A be the event that the first selected CD is scratched and the second selected CD can be read and played properly. Now, explicitly list all the outcomes in the sample space Ohm and in A below. Then find P(A) = #A/# Ohm and give it as a simple fraction in the box below.

Solution

a)

Omega = {(c1, c2), (c2, c3), (c1, c3), (c2, c1), (c3, c2), (c3, c1)}

b)

A = {(c3, c1), (c3, c1)}

c)

The sample space Omega has 6 elements, and A has 2 elements. Thus,

P(A) = 2/6 = 1/3 or 0.3333333 [ANSWER]