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? $\frac{2}{11}$ $\frac{3}{11}$ $\frac{5}{11}$ $\frac{6}{11}$

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? $\frac{2}{11}$ $\frac{3}{11}$ $\frac{5}{11}$ $\frac{6}{11}$

Answer

Answer:

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

Explanation:

Step1: Count shaded marbles

There are 5 shaded marbles.

Step2: Count marbles labeled with multiple of 3

Marbles labeled 3, 6, 9 are multiples of 3. There are 3 such marbles.

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

Marbles 3 and 9 are both shaded and multiples of 3. There are 2 such marbles.

Step4: Use the inclusion - exclusion principle

$P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Here, $P(A)=\frac{5}{11}$, $P(B)=\frac{3}{11}$, $P(A\cap B)=\frac{2}{11}$. So $P(A\cup B)=\frac{5 + 3- 2}{11}=\frac{6}{11}$.