The probability that the first marble chosen is shaded and the second marble chosen is labeled with an odd number is <u>24/121</u>, making the <u>2nd option</u> the right choice.
In the question, we are given that a bag contains eleven equally sized marbles, which are numbered. Two marbles are chosen at random and replaced after each selection.
We are asked to find the probability that the first marble chosen is shaded and the second marble chosen is labeled with an odd number.
For the first selection:
The number of shaded marbles = 4 {viz. 1, 3, 4, and 9}.
The total number of marbles = 11.
Thus, the probability of choosing a shaded marble in the first selection = 4/11.
For the second selection:
The number of odd-numbered marbles = 6 {viz. 1, 3, 5, 7, 9, 11}.
The total number of marbles = 11 {Since the marble in the first selection has been replaced}.
Thus, the probability of choosing an odd-numbered marble in the second selection = 6/11.
Thus, the probability that the first marble chosen is shaded and the second marble chosen is labeled with an odd number = 4/11 * 6/11 = 24/121.
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