Question

a jar contains 4 red marbles numbered 1 to 4 and 8 blue marbles numbered 1 to 8. a marble is drawn at random from the jar. find the probability of the given event. write your answers as reduced fractions. (a) the marble is red your answer is : (b) the marble is odd-numbered your answer is : (c) the marble is red or odd-numbered your answer is : (d) the marble is blue and even-numbered your answer is :

Answer 1

There are 14 marbles over all. 10 of them are blue and 7 even numbered (half of each batch is even numbered this gives 10/2+4/2=7). So the chance that a given a random marble is blue is 10/14=5/7, they chance that is even numbered is 7/14=1/2, the chance that it is both blue and even numbered is 5/14 ((1/2)*(5/7)), bringing us to a total of 5/7+1/2–5/14=10/14+7/14–5/14=12/14=6/7.