Statistics

Question

An urn contains 3 white marbles and 2 black marbles. Two marbles are drawn without replacement. What is the probability that the first marble drawn is white OR the second is black?

Answer 1

Prob_white (3/5) = 60% = .6

 

 

Prob_{not white}(2/5) Prob_black(1/4) =

            2/20 = 10% = .1

 

The first draw will be white = 3/5 = 60%

 

The first draw not white = 2/5 = 40%

 

If the first is not white, then it is black,

leaving one black to be drawn out of 4 marbles,

drawing a black on the second draw is 1/4 = 25%, 

multiply this by the probability NOT WHITE on 

first draw = .4(.25) = .1

 

Probability of White on first draw OR Black on second draw is:

 

      .6 + .1 = .7 = 70%