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?
prob(1st is white) = 8/18
there are now 17 left of which 10 are black , so
prob(2nd black) = 10/17
so prob (of your event) = (8/18)(10/17) = 40/153
@reiny omg ty so much
To find the probability that the first marble drawn is white and the second marble drawn is black, we can break down the problem into two steps:
Step 1: Finding the probability of drawing a white marble first.
Step 2: Finding the probability of drawing a black marble second, given that a white marble was drawn first.
Step 1:
In the urn, there are 8 white marbles and 18 marbles in total (8 white + 10 black). So the probability of drawing a white marble on the first draw is:
P(white first) = Number of favorable outcomes / Total number of outcomes
= 8 white marbles / 18 total marbles
= 4/9
Step 2:
After removing a white marble from the urn, there are now 7 white marbles remaining along with 10 black marbles. The total number of marbles is now 17 (7 white + 10 black). So the probability of drawing a black marble on the second draw, given that a white marble was already drawn first, is:
P(black second | white first) = Number of favorable outcomes / Total number of outcomes
= 10 black marbles / 17 remaining marbles
= 10/17
To find the probability of both events occurring, we multiply the probabilities from each step:
P(white first and black second) = P(white first) * P(black second | white first)
= (4/9) * (10/17)
≈ 0.235
Therefore, the probability that the first marble drawn is white and the second marble drawn is black is approximately 0.235 or 23.5%.
To determine the probability of drawing a white marble first and a black marble second, you need to use the concept of conditional probability. Conditional probability is the probability of an event occurring given that another event has already occurred. In this case, we want to find the probability of drawing a black marble second, given that we have already drawn a white marble first.
To calculate the probability, you can follow these steps:
Step 1: Determine the number of white marbles in the urn. In this case, there are 8.
Step 2: Determine the total number of marbles in the urn. Here, there are 8 white marbles + 10 black marbles, giving a total of 18 marbles.
Step 3: Calculate the probability of drawing a white marble first. Since there are 8 white marbles out of 18 total marbles, the probability is 8/18, which can be simplified to 4/9.
Step 4: After drawing a white marble, you now have 7 white marbles and 10 black marbles remaining in the urn. So, there are 7 white marbles and 10 black marbles out of a total of 17 marbles.
Step 5: Calculate the probability of drawing a black marble second, given that a white marble was already drawn. The probability is 10/17.
Step 6: Multiply the probability of drawing a white marble first (4/9) by the probability of drawing a black marble second (10/17).
(4/9) * (10/17) = 40/153.
Therefore, the probability of drawing a white marble first and a black marble second is 40/153.