Question

a number cube is rolled and a quarter is tossed.Find P(even number and heads)

Answer 1

Assume that the cube and the quarter are fair, that is
for each number 1..6
the probability to get it on the cube is the same
and equal to 1/6, and also
the probability to get either head or tail on
the coin is the same
1/2.

Hence the probability to get an even number on the cube is

P(even number) = P(2) + P(4) + P(6) = 1/6 * 3 = 1/2.


Moreover,
assume that rolling of the cube and tossing of a quarter are
independent,
hence
P(even number and heads) = P(even number) *
P(heads)
= 1/2 * 1/2 = 1/4.