a bag contains eleven equally sized marbles, which are numbered. what is the probability that a marble…

a bag contains eleven equally sized marbles, which are numbered. what is the probability that a marble chosen at random is shaded or is labeled with a multiple of 3?\n○ $\frac{2}{11}$\n○ $\frac{3}{11}$\n○ $\frac{5}{11}$\n○ $\frac{6}{11}$

a bag contains eleven equally sized marbles, which are numbered. what is the probability that a marble chosen at random is shaded or is labeled with a multiple of 3?\n○ $\frac{2}{11}$\n○ $\frac{3}{11}$\n○ $\frac{5}{11}$\n○ $\frac{6}{11}$

Answer

Answer:

D. $\frac{6}{11}$

Explanation:

Step1: Count shaded marbles

There are 4 shaded marbles.

Step2: Count marbles labeled with multiple of 3

The multiples of 3 among 1 - 11 are 3, 6, 9. So there are 3 marbles labeled with a multiple of 3.

Step3: Count marbles that are both shaded and multiple of 3

The marbles that are both shaded and multiple of 3 are 3 and 9. So there are 2 such marbles.

Step4: Use the addition - rule of probability

The formula for $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Here, $A$ is the event of choosing a shaded marble and $B$ is the event of choosing a marble labeled with a multiple of 3. The total number of marbles $n = 11$. $P(A)=\frac{4}{11}$, $P(B)=\frac{3}{11}$, $P(A\cap B)=\frac{2}{11}$. Then $P(A\cup B)=\frac{4 + 3- 2}{11}=\frac{5}{11}$.