Question

An urn contains two red and two green marbles. we pick one marble, record its color, and replace it before picking the second marble. we repeat this procedure a third time. the probability distribution for the number of red marbles is given by number of red marbles 0 1 2 3 probability 1/8 3/8 3/8 1/8 for this distribution, the probability two or more red marbles is given by:

Answer 1

`P(X \geq 2) = (1)/(2)`

Explanation:

Our probability density function indicates that:

`P(X = 0) = (1)/(8)`

`P(X = 1) = (3)/(8)`

`P(X = 2) = (3)/(8)`

`P(X = 3) = (1)/(8)`

the probability two or more red marbles is given by

`P(X \geq 2) = P(X = 2) + P(X = 3) = (3)/(8) + (1)/(8) = (4)/(8) = (1)/(2)`