A bag contains 2 white marbles and 7 purple marbles. Two marbles are drawn at random. One marble is drawn and not replaced. Then a second marble is drawn.
Is there a greater chance of selecting two white marbles in a row or two purple marbles in a row?
To calculate the probability of each event, let's first find the probability of selecting two white marbles in a row.
There are 2 white marbles out of 9 total marbles, so the probability of selecting a white marble on the first draw is 2/9. After drawing one white marble, there is 1 white marble left out of 8 total marbles, so the probability of selecting a white marble on the second draw is 1/8. To find the probability of both events happening consecutively, we multiply the probabilities: (2/9) * (1/8) = 2/72.
Now let's find the probability of selecting two purple marbles in a row.
There are 7 purple marbles out of 9 total marbles, so the probability of selecting a purple marble on the first draw is 7/9. After drawing one purple marble, there are 6 purple marbles left out of 8 total marbles, so the probability of selecting a purple marble on the second draw is 6/8 = 3/4. To find the probability of both events happening consecutively, we multiply the probabilities: (7/9) * (3/4) = 21/36.
Comparing the probabilities, we can see that there is a greater chance of selecting two purple marbles in a row (21/36) than two white marbles in a row (2/72).