Suppose we have four boxes. A, B, C and D containing coloured marbles as given below: Box Marble colour Red White Black A 1 6 3 B 6 2 2 C 8 1 1 D 0 6 4 One of the boxes has been selected at random and a single marble is drawn from it. If the marble is red, what is the probability that it was drawn from box A?, box B?, box C?
Let R be the event of drawing the red marble.
Let E A , E B and E C respectively denote the event of selecting the box A, B and C.
Total number of marbles = 40 .
Number of Red marbles = 15 .
The probability of getting the red marble is given by,
P ( R ) = 15 40 = 3 8
The probability of drawing the red marble from Box A is given by,
P ( E A | R ) = P ( E A ∩ R ) P ( R ) = 1 40 3 8 = 1 15
The probability of drawing the red marble from Box B is given by,
P ( E B | R ) = P ( E B ∩ R ) P ( R ) = 6 40 3 8 = 2 5
The probability of drawing the red marble from Box C is given by,
P ( E C | R ) = P ( E C ∩ R ) P ( R ) = 8 40 3 8 = 8 15
Thus, the probability of drawing the red marble from Box A, B and C respectively is 1 15 , 2 5 and 8 15 .
Let
Let
Total number of marbles
Number of Red marbles
The probability of getting the red marble is given by,
The probability of drawing the red marble from Box A is given by,
The probability of drawing the red marble from Box B is given by,
The probability of drawing the red marble from Box C is given by,
Thus, the probability of drawing the red marble from Box A, B and C respectively is
