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?

Rationale

The probability that Debra grabs 2 socks of the same color is 1/3.

To find the probability of selecting 2 socks of the same color, we calculate the total combinations of sock pairs and the successful outcomes. In this case, there are 3 total socks, leading to 3 possible pairs, of which only 1 pair consists of the same color (the black socks).

A ({1/3}) CORRECT

This choice correctly represents the probability of selecting 2 black socks from the drawer. There are 3 total combinations of socks (BB, BR, and BR) and only 1 combination where the socks are the same color (BB). Thus, the probability is calculated as 1 (successful outcome) divided by 3 (total outcomes), resulting in 1/3.

B ({2/3}) YOUR ANSWER

This option incorrectly suggests a higher likelihood of choosing 2 socks of the same color. While there are 2 black socks, the probability of choosing 2 socks of the same color cannot exceed the actual successful outcomes available. The correct calculation shows that only 1 out of 3 combinations results in the same color, making this choice inaccurate.

C ({3/3}) YOUR ANSWER

Choosing 3/3 implies that Debra will always pick 2 socks of the same color, which is not possible given that there is 1 brown sock present. Since there is only a single successful outcome out of three possible pair combinations, this choice overestimates the probability entirely.

D ({3/2}) YOUR ANSWER

This option is mathematically invalid as probabilities cannot exceed 1. The value of 3/2 suggests a certainty greater than 100%, which contradicts the principles of probability. The maximum probability for any event is 1 (or 100%), ruling out this choice entirely.

Conclusion

The probability of Debra grabbing 2 socks of the same color is indeed 1/3, as there is only one successful pairing of the same color (the two black socks) among three possible pairings. The other options miscalculate or misunderstand the nature of probability, illustrating the importance of careful consideration in probability assessments.

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?

The probability that Debra grabs 2 socks of the same color is 1/3.

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