Final answer:
After calculating the probability of selecting 2 red and 2 blue chips from a box containing 5 red and 7 blue chips, the answer is found to be 0.4242. This does not match any of the provided options, indicating a possible error in the question or options. The calculation involves combinatorics and the use of the combination formula.
Step-by-step explanation:
The question asks for the probability of selecting 2 red chips and 2 blue chips from a box containing 5 red chips and 7 blue chips, in total 4 chips are drawn without replacement. To calculate this, we can use combinatorics. The number of ways to select 2 reds out of 5 is given by the combination formula C(5,2), similarly for blue chips it's C(7,2). The total number of ways to draw 4 chips out of 12 is C(12,4). The desired probability is the number of ways to select the 2 red and 2 blue chips divided by the total number of ways to select any 4 chips.
The calculations are as follows:
- C(5,2) = 10
- C(7,2) = 21
- C(12,4) = 495
So, the probability P(2 red and 2 blue) is:
P(2R, 2B) = (C(5,2) * C(7,2)) / C(12,4) = (10 * 21) / 495
After calculation, P(2R, 2B) = 0.4242
However, this does not match any of the given options A, B, C, or D. Hence, there might be a misunderstanding or a typo in the question or options. If the calculation is correct, the probability should be rounded off to three decimal places as given in the question, but none of the provided options match the calculated result.