a bag contains eleven equally - sized marbles, which are numbered. two marbles are chosen at random and…

Explanation:

Step1: Calculate probability of first event

There are 4 shaded marbles out of 11 marbles. So the probability of choosing a shaded marble first, denoted as $P(A)$, is $\frac{4}{11}$.

Step2: Calculate probability of second event

There are 6 odd - numbered marbles out of 11 marbles. So the probability of choosing an odd - numbered marble second, denoted as $P(B)$, is $\frac{6}{11}$.

Step3: Use multiplication rule for independent events

Since the marbles are replaced after each selection, the two events are independent. The probability of both events occurring is $P(A)\times P(B)$. So $P = \frac{4}{11}\times\frac{6}{11}=\frac{24}{121}$.

Answer:

$\frac{24}{121}$