What is the probability of selecting a white marble and then picking a striped marble without replacement if there are 4 white 3 black and 3 striped
10 marbles in all, so
4/10 * 3/9
To find the probability of selecting a white marble and then picking a striped marble without replacement, you need to first determine the total number of marbles and then calculate the probability for each event.
Step 1: Calculate the total number of marbles:
The total number of marbles is the sum of the white, black, and striped marbles:
Total marbles = number of white marbles + number of black marbles + number of striped marbles
Total marbles = 4 white marbles + 3 black marbles + 3 striped marbles
Total marbles = 10 marbles
Step 2: Calculate the probability of selecting a white marble:
The probability of selecting a white marble is the number of white marbles divided by the total number of marbles:
Probability of selecting a white marble = number of white marbles / total marbles
Probability of selecting a white marble = 4 white marbles / 10 marbles
Probability of selecting a white marble = 2/5 or 0.4
Step 3: Calculate the probability of picking a striped marble after selecting a white marble (without replacement):
After selecting a white marble, there are now 9 marbles remaining: 3 black marbles and 3 striped marbles (since you do not replace the marble). The probability of picking a striped marble is the number of striped marbles divided by the new total number of marbles:
Probability of picking a striped marble = number of striped marbles / new total marbles
Probability of picking a striped marble = 3 striped marbles / 9 marbles
Probability of picking a striped marble = 1/3 or 0.333
Step 4: Calculate the combined probability:
The combined probability is the product of the probability of selecting a white marble and the probability of picking a striped marble:
Combined probability = Probability of selecting a white marble * Probability of picking a striped marble
Combined probability = 0.4 * 0.333
Combined probability = 0.1332 or approximately 0.133, rounded to three decimal places.
Therefore, the probability of selecting a white marble and then picking a striped marble without replacement, given that there are 4 white marbles, 3 black marbles, and 3 striped marbles, is approximately 0.133.