Question

A bag of 11 marbles contains 5 marbles with red on them, 4 with blue on them 5with green on themand 3 with red and green on them What is the probability that a randomly chosen marble has either green or red on it? Note that these events are not mutually exclusive Express your answer as a fraction in lowest terms or a decimal rounded to the nearest

Answer 1

Step-by-step explanation:

Step-by-step explanation:

Let's denote the events as follows:

R = a red marble is chosen

G = a green marble is chosen

The information provided is:

`\begin{gathered} n(R)=5 \\ n(G)=5 \\ n(R\cap G)=3 \end{gathered}`

Total number of marbles in the bag is,

`n(S)=11`

The probability of an event E is:

`\begin{gathered} Pr(E)=(n(E))/(n(S)) \\ Pr(R\cup G)=Pr(R)+Pr(G)-Pr(R\cap G) \\ Pr(R\cup G)=(5)/(11)+(5)/(11)-(3)/(11) \\ Pr(R\cup G)=(7)/(11) \end{gathered}`

Hence,

The final answer is

`(7)/(11)`