Question

A bag of 11 marbles contains 7 marbles with red on them, 6 with blue on them, 6 with green on them, and 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 millionth.

Answer 1

In the case of two not mutually exclusive events, we have that, given events A and B,

`P(A\lor B)=P(A)+P(B)-P(A\cap B)`

Notice that if we only include the first two contributions, we would count the intersection of the two events twice; therefore, we must subtract the probability of its intersection once.

In our case,

`P(R\lor G)=(7)/(11)+(6)/(11)-(3)/(11)=(10)/(11)`

Therefore, the answer is 10/11.