Question

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

Explanation:

Step1: Count shaded marbles

There are 5 shaded marbles.

Step2: Count marbles labeled with multiple of 3

The multiples of 3 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, \(n(A) = 5\), \(n(B)=3\), \(n(A\cap B)=2\) and total number of marbles \(n = 11\). So \(P(A\cup B)=\frac{5 + 3-2}{11}=\frac{6}{11}\).

Answer:

\(\frac{6}{11}\)