A box contains 5 purple marbles 3 green marbles and 2 orange marbles. Two consecutive draws are made from the box without replacement for the first draw. Find the probability of each event
First, let's find the probability of drawing a purple marble and then a green marble.
The probability of drawing a purple marble on the first draw is 5/10 (since there are 5 purple marbles out of a total of 10 marbles). After the first purple marble is drawn, there are now 9 marbles left in the box, with 3 of them being green. So the probability of drawing a green marble on the second draw, given that a purple marble was drawn first, is 3/9.
Therefore, the probability of drawing a purple marble and then a green marble is:
(5/10) * (3/9) = 1/6
Next, let's find the probability of drawing an orange marble and then another orange marble.
The probability of drawing an orange marble on the first draw is 2/10. After the first orange marble is drawn, there are now 9 marbles left in the box, with only 1 of them being orange. So the probability of drawing another orange marble on the second draw, given that an orange marble was drawn first, is 1/9.
Therefore, the probability of drawing an orange marble and then another orange marble is:
(2/10) * (1/9) = 1/45
Thus, the probabilities of the two events are:
1. Drawing a purple marble and then a green marble: 1/6
2. Drawing an orange marble and then another orange marble: 1/45