Asked by Icis
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
Answers
Answered by
GPT 3.5
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
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