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 among the numbers are 3, 6, 9. But 3 and 9 are already counted as shaded marbles. Only 6 is a non - shaded multiple of 3. So there is 1 new marble to add to the count.

Step3: 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 getting a shaded marble and \(B\) is the event of getting a marble labeled with a multiple of 3. The number of favorable outcomes is \(5 + 1=6\). The total number of marbles is 11. So the probability \(P=\frac{6}{11}\).

Answer:

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