3. An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events:
B: occurs on either die
Sample space when a die is rolled:
S = {1, 2, 3, 4, 5, 6}
Let E = Event of rolling a pair of dice (= Event that a die is rolled twice!) [6x6 = 36 possible outcomes]
E = [ {(x,y): x,y S } ] = {(1,1), (1,2)...(1,6),(2,1).....(6,5),(6,6)}
Now,
B: 2 occurs on either die
Hence the number 2 can come on first die or second die or on both the die simultaneously.
B = [ {(a,b): (a,b) E, a or b = 2 } ]= {(1,2), (2,2), (3, 2), (4,2), (5,2), (6,2), (2,1), (2,3), (2,4), (2,5), (2,6)}