A bag contains 9 spherical objects 1 red 3 white and 5 blue

A bag contains 9 spherical objects, 1 red, 3 white and 5 blue. The objects are randomly drawn from the bag without replacement until a white object is drawn. Let X be the random variable counting the number of objects drawn from the bag.

a) Is X a finite, infinite discrete or countinous random variable?

A bag contains 9 spherical objects, 1 red, 3 white and 5 blue. The objects are randomly drawn from the bag without replacement until a white object is drawn. Let X be the random variable counting the number of objects drawn from the bag. a) Is X a finite, infinite discrete or countinous random variable? b) Calculate P(X

Solution

a)

Finite since there are only nine objects.

Discrete as it takes only integer values

b)

P(X <=2) = P( X=1 ) + P( X=2)

           = P( first drawn is white) + P( first drawn is non-white and second is white)

             = 3/9 + (6/9)*(3/8)

           = 1/3 + 1/4 = 7/12 = 0.58333