Question

Assume a jar has five red marbles and four black marbles. Draw out two marbles with and without replacement. Find the requested probabilities. (Enter the probabilities as fractions.)

(a)    P(two red marbles)

with replacement
without replacement

(b)    P(two black marbles)

with replacement
without replacement

(c)    P(one red and one black marble)

with replacement
without replacement

(d)    P(red on the first draw and black on the second draw)

with replacement
without replacement

Answer 1

a) P(two red marbles with replacement) = 5/9 x 5/9 = 25/81

P(two red marbles without replacement) = 5/9 x 4/8 = 5/18

b) P(two black marbles with replacement) = 4/9 x 4/9 = 16/81

P(two black marbles without replacement) = 4/9 x 3/8 = 1/6

c) P(one red marble and one black marble with replacement) = 2 x 5/9 x 4/9 = 40/81

P(one red marble and one black marble without replacement) = 2 x 5/9 x 4/8 = 5/9

d)  P(red on the first draw and black on the second draw with replacement) = 5/9 x 4/9 = 20/81

P(red on the first draw and black on the second draw without replacement) = 5/9 x 4/8 = 5/18