I do not understand how to figure out probability.
Lee has an urn with 8 white marbles and 10 black marbles. A marble is drawn at random and not replaced. Then a second marble is drawn randomly. What is the probability that the first is white and the second is black?
To calculate the probability of an event, you need to divide the number of favorable outcomes by the total number of possible outcomes. In this case, the favorable outcome is drawing a white marble first and a black marble second. Let's break down the steps of calculating the probability in this particular scenario:
Step 1: Determine the total number of marbles in the urn. In this case, there are 8 white marbles + 10 black marbles = 18 total marbles.
Step 2: Calculate the probability of drawing a white marble first. Since there are 8 white marbles out of 18 total marbles, the probability of drawing a white marble first is 8/18.
Step 3: After drawing the first marble, one marble is removed from the urn, so there are now 17 marbles left in total.
Step 4: Calculate the probability of drawing a black marble second. Now, there are 10 black marbles left out of the 17 total marbles, so the probability of drawing a black marble second is 10/17.
Step 5: Multiply the probabilities of the individual events together to find the joint probability. The probability of drawing a white marble first and a black marble second is (8/18) * (10/17).
Step 6: Simplify the expression if possible. In this case, we can reduce the fraction by dividing both the numerator and denominator by 2: (4/9) * (5/17).
Step 7: Multiply the fractions: 4/9 * 5/17 = 20/153.
Step 8: Convert the fraction into decimal or percentage form for better understanding. In this case, 20/153 is approximately 0.1307, which is about 13.07% (rounded to two decimal places).
Therefore, the probability that the first marble drawn is white and the second marble drawn is black is approximately 0.1307 or 13.07%.