Can somebody help me solve this problem ? I am not so good with probability. -
A bag contains 2 green marbles and 3 white marbles. One marble is drawn at random and not replaced.
Then a second marble is drawn. What is the probability that the first marble is white and the second one
is green?
Prob(white, then green)
= (3/5)(2/4) = 3/10
Can you tell where my numbers came from ?
3/5 came from the probability of drawing White marbles. I am not sure about the (2/4)
since you kept the first marble drawn, there are now only 4 left, but the 2 greens are still in there
so 2/4 for the greens
Okay , that makes sense .
Certainly! I'd be happy to help you solve this probability problem step by step.
To find the probability that the first marble drawn is white and the second one is green, we can break it down into two steps.
Step 1: Find the probability of drawing a white marble first.
Step 2: Find the probability of drawing a green marble second, given that the first marble was white.
Step 1: Probability of drawing a white marble first
We know that there are a total of 2 green marbles and 3 white marbles, so the probability of drawing a white marble first can be calculated by dividing the number of favorable outcomes (white marbles) by the total number of possible outcomes (total marbles).
Total marbles = number of green marbles + number of white marbles = 2 + 3 = 5
Favorable outcome = number of white marbles = 3
So, the probability of drawing a white marble first is 3/5.
Step 2: Probability of drawing a green marble second, given that the first marble was white
Now, we need to find the probability of drawing a green marble given that the first marble drawn was white. However, since the first marble is not replaced, the total number of marbles decreases by 1.
After the first white marble is drawn, there are 4 marbles left in the bag (2 green and 2 white). The probability of drawing a green marble second can be calculated in the same way as we did in Step 1: dividing the number of favorable outcomes (green marbles) by the total number of possible outcomes (total marbles).
Total marbles = number of green marbles + number of white marbles = 2 + 2 = 4
Favorable outcome = number of green marbles = 2
So, the probability of drawing a green marble second, given that the first marble was white, is 2/4.
Now, we can find the probability of both events happening by multiplying the probabilities of the two steps together:
Probability of drawing a white marble first * Probability of drawing a green marble second, given that the first marble was white
= (3/5) * (2/4)
= 6/20
= 3/10
Therefore, the probability that the first marble is white and the second one is green is 3/10.
I hope this explanation helps you understand how to approach this probability problem. If you have any further questions, feel free to ask!