1. There are 3 socks in Debra's drawer, 2 black and 1 brown. If she randomly grabs 2 socks from the drawer without looking, what is the probability that they are the same color?
Answer: A
The probability that Debra grabs two socks of the same color is 1/3.
When Debra randomly selects 2 socks from her drawer, the likelihood that both socks are of the same color can be calculated. Given that there are 2 black socks and 1 brown sock, the probability of selecting 2 socks of the same color is indeed 1/3.
A) 1/3
This option is correct because the only way for Debra to grab two socks of the same color is to select both black socks. The total combinations of grabbing any two socks from the three available is 3 (BB, BR, and BR), with only one combination resulting in the same color (BB). Therefore, the probability is 1 out of the 3 possible combinations.
B) 2/3
This option is incorrect as it suggests that there is a higher likelihood of selecting two socks of the same color. The actual calculations show that only one combination (the two black socks) out of three possible combinations yields socks of the same color, hence the probability cannot be 2/3.
C) 3/3
This option is incorrect because a probability of 3/3 implies that it is certain that the two socks will always be of the same color, which is not the case. Given the presence of a brown sock, there are combinations that result in socks of different colors, making the probability less than 1.
D) 3/2
This option is not a valid probability as it exceeds the maximum possible value of 1. Probabilities cannot exceed 1, and thus this option is mathematically incorrect and does not apply to the context of the problem.
Conclusion
In summary, the correct answer is 1/3, as it accurately reflects the probability of selecting two socks of the same color from Debra's drawer. All other options either miscalculate the combinations or provide impossible probabilities, reinforcing that only option A is valid based on the given scenario.