A jar contains 8 red marbles numbered 1 to 8 and 8 blue marbles numbered 1 to 8. A marble is drawn atrandom from the jar. Find the probability of the given event, please show your answers as reducedfractions.(a) The marble is red. P(red)%D(b) The marble is odd-numbered. P(odd)=2(c) The marble is red or odd-numbered. P(red or odd) =(d) The marble is blue or even-numbered. P(blue or even) =Submit Questione to search803/41/2

a) There are 8 red marbles numbered 1 to 8 and 8 blue marbles numbered 1 to 8. Consider an event R that defines the red marbles and another event B, that defines the blue marbles.Hence, n(R) = 8 and n(B) = 8. Hence, the total number of marbles is, n = 16 (= 8 + 8). Hence, the probability that a marble is red is n(R)/n = 8/16 = 1/2. b) There are total 4 (= 8/2) odd numbers in red marbles and 4 (= 8/2) odd numbers in blue marbles. Consider another event O, that defines the odd numbers. Thus, the total odd numbered marbles is n(O) = 4 + 4 = 8. Thus, the probability that a marble is odd-numbered is, P(O) = P(odd) = n(O)/n = 8/16 = 1/2. c) There are total 4 red and odd- numbered marbles. The probability that marble is red or odd-numbered is, P(R or O) = P(red or odd) = P(red) + P(odd) – P(red and odd) = 8/16 + 8/16 – 4/16 = 12/16 = 3/4. d) There are total 4 (= 8/2) even numbers (2, 4, 6, 8) in red marbles and 4 (= 8/2) even numbers (2, 4, 6, 8) in blue marbles. Consider another event E, that defines the even numbers. Thus, the total even numbered marbles is n(E) = 4 + 4 = 8. There are total 4 blue and even- numbered marbles. The probability that marble is blue or even-numbered is, P(B or E) = P(blue or even) = P(blue) + P(Even) – P(blue and even) = 8/16 + 8/16 – 4/16 = 12/16 = 3/4.