Question

4-18.    Use the equally likely sample space to compute the probability of the following outcome when rolling a pair of dice: The number on the first die is even or the number on the second die is even.     

Answer 1

Rolling pair of dice:

Case 1:
Let

A = Number on the first die = even

Total number of events = 6

Favorable events: 2, 4, 6: 3 Nos.

So,

P(A) = 3/6 = 0.5

Case 2:
Let

B = Number on the second die = even

Total number of events = 6

Favorable events: 2, 4, 6: 3 Nos.

So,

P(B) = 3/6 = 0.5

Case 3:

A AND B = Number on the first die = even AND Number on the second die = even

Total number of events = 6 X 6 = 36

Favorable events: (2,2), (4,4), (6,6): 3 Nos.

So,

P(A AND B) = 3/36 = 0.0833

By Generalized Addition Theorem:
P(Number on the first die is even OR Number on the first die is even) = P(Number on the first die is even) + P(Number on the second die is even) - P(Number on the first die is even AND Number on the second die is even)

= 0.5 + 0.5 - 0.0833

=0.9167

So,

Answer is:

0.9167