From the information given, the jar contains 8 red marbles and 12 blue marble. The marbles are
Red = 1, 2, 3, 4, 5, 6, 7, 8
Blue = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
Probability = number of favorable outcomes/number of total outcomes
number of total outcomes = 8 + 12 = 20
a) number of red marbles = 8
the probability that the marble is red, P(red)= 8/20
Dividing the numerator and denominator by 4,
P(red) = 2/5
b)odd-numbered marbles are
Red = 1, 3, 5, 7
Blue = 1, 3, 5, 7, 9, 11
number of odd-numbered marbles = 10
P(odd) = 10/20
Dividing the numerator and denominator by 10,
P(odd) = 1/2
c) The events can occur together. This means that they are not mutually exclusive. Thus,
P(red or odd) = P(red) + P(odd) - P(red and odd)
P(red and odd) = 4/20
P(red or odd) = 2/5 + 1/2 - 4/20
P(red or odd) = 14/20
Dividing the numerator and denominator by 2,
P(red or odd) = 7/10
d) P(blue or even) = P(blue) + P(even) - P(blue and even)
P(blue) = 12/20
P(even) = 1 - P(odd) = 1 - 1/2 = 1/2
P(blue and even) = 6/20
P(blue or even) = 12/20 + 1/2 - 6/20
P(blue or even) = 16/20
Dividing the numerator and denominator by 4,
P(blue or even) = 4/5