Maria will pick two red marbles from a bag containing 4 red marbles, 2 white marbles, and 2 black marbles. Consider the following compound events:
Maria will pick two red marbles if she returns the first marble:
[tex]P((\text { red })) P((\text { red }))=\left(\frac{4}{8}\right)\left(\frac{4}{8}\right)[/tex]
Maria will pick up two red marbles in a row if she did not replace the first marble:
[tex]P((\text { red })) P((\text { red }))=\left(\frac{4}{8}\right)\left(\frac{3}{7}\right)[/tex]
Answer (1)
The problem is based on the false premise of having red marbles in the bag. Therefore, it is impossible to calculate the probabilities as intended. The problem needs to be revised with correct information about the bag's contents.
Explanation
Analyze the problem and identify the inconsistency The problem is incomplete. It refers to picking 'red' marbles, but the bag contains only white and black marbles. Therefore, it's impossible to calculate the probability of picking two red marbles based on the given information. The provided calculations, P (( red )) P (( red )) = ( 8 4 ) ( 8 4 ) and P (( red )) P (( red )) = ( 8 4 ) ( 7 3 ) , are based on incorrect assumptions about the bag's contents.
Explain why the calculations are not applicable Since the problem is based on a false premise (the existence of red marbles), we cannot proceed with any meaningful calculations. The probabilities provided are not applicable to the actual contents of the bag.
Conclude that the problem cannot be solved as is Due to the inconsistency in the problem statement (mentioning red marbles when only white and black marbles are present), it is impossible to provide a valid solution. The problem needs to be corrected to accurately reflect the contents of the bag before any probability calculations can be made.
Examples
This problem highlights the importance of carefully checking the initial conditions before performing any calculations. In probability, as in many areas of math and science, starting with incorrect information will inevitably lead to incorrect results. Always ensure that your assumptions align with the given data before proceeding.
