There are 4 black marbles and 2 white marbles in a bag. What is the probability of choosing a black marble,not replacing it, then choosing a white marble.
1st; 1 black from 6 marbles when you have 4 black is 4chances out of 6 total marbles ie is 4/6
2nd; one white when you have a choice of 2 out of a total of 5 marbles; ie 2/5 Therefore the sum will be
4/6 x 2/5 = 8/30
= 4/15
To find the probability of choosing a black marble, not replacing it, and then choosing a white marble, we need to calculate the probability of each individual event and multiply them together.
Step 1: Calculate the probability of choosing a black marble:
We have 4 black marbles out of a total of 6 marbles in the bag.
So, the probability of choosing a black marble is 4/6 = 2/3.
Step 2: Calculate the probability of choosing a white marble after not replacing the black marble:
After selecting a black marble, there will be 5 marbles left in the bag, with 1 white marble.
So, the probability of choosing a white marble is 1/5.
Step 3: Multiply the probabilities of the two events:
To find the probability of both events occurring, we multiply their probabilities:
(2/3) * (1/5) = 2/15.
Therefore, the probability of choosing a black marble, not replacing it, and then choosing a white marble is 2/15.
To calculate the probability of choosing a black marble and then choosing a white marble without replacement, we need to determine the number of favorable outcomes (choosing a black marble first and then a white marble) and the total number of possible outcomes.
First, let's determine the total number of marbles in the bag (considering both black and white marbles). In this case, there are a total of 6 marbles (4 black + 2 white).
To calculate the probability of the first event (choosing a black marble), we divide the number of black marbles by the total number of marbles:
Probability of choosing a black marble = Number of black marbles / Total number of marbles
Probability of choosing a black marble = 4 / 6
After choosing a black marble, we have 3 black marbles and 2 white marbles left. Therefore, the total number of marbles decreases to 5 (3 black + 2 white).
To calculate the probability of the second event (choosing a white marble after choosing a black marble), we divide the number of white marbles by the total number of marbles:
Probability of choosing a white marble = Number of white marbles / Total number of marbles
Probability of choosing a white marble = 2 / 5
Since the two events (choosing a black marble and then choosing a white marble) are dependent on each other and occur consecutively, we multiply the probabilities of the individual events to find the combined probability:
Probability of choosing a black marble and then choosing a white marble = Probability of choosing a black marble * Probability of choosing a white marble
Probability of choosing a black marble and then choosing a white marble = (4 / 6) * (2 / 5)
Hence, the probability of choosing a black marble and then choosing a white marble without replacement is 4/15, or approximately 0.267.