Question

1. A jar contains 5 red marbles numbered 1 to 5 and 6 blue marbles numbered 1 to 6. A marble is drawn at random from the jar. Find the probability that the marble is blue or odd-numbered.

Answer 1

We will use the following formula:

`P(A\cup B)=P(A)+P(B)-P(A\cap B).`

First, we compute the probability that we get a blue marble:

`P(\text{Blue)}=(6)/(5+6)=(6)/(11)\text{.}`

Now, we compute the probability of getting an odd-numbered marble:

`P(\text{odd-num)}=(6)/(11)\text{.}`

Finally, the probability that we draw a blue and odd-numbered marble is:

`P(\text{blue and odd)=}(3)/(11).`

Answer: The probability that the marble is blue or odd-numbered is:

`\begin{gathered} P(\text{blue or odd)=P(blue)+P(odd-num)-P(blue and odd)=}(6)/(11)+(6)/(11)-(3)/(11)=(9)/(11). \\ P(\text{blue or odd)}=(9)/(11)\text{.} \end{gathered}`