Question

A box contains three cokes and two beers (root beer of course). Julie draws at random twice without replacement from the box. (Any draw is equally likely)

a.) What is the probability that she gets at least one beer?

b.) What is the probability that she drew a coke on the first draw given that she drew a beer on the second draw?

Please explain step by step!

Answer 1

Solution:

number of cokes = 3

number of beers = 2

total number of samples = 3 + 2 = 5

total possibilities = (cc), (cb), ( bc), (bb)

( a )

possibilities of drawing atleast one beer = (cb),(bc),(bb)

probability that she gets at least one beer = (3/5)(2/4) + (2/5)(3/5) + (2/5)(1/4)

= 0.3+0.3 + 0.1

= 0.7

( b )

possibilities of drawing beer in second draw = (cb),(bb)

probability of drewing a coke in first draw given that she drew a beer on the second draw

= ((3/5)(2/4))/ ((3/5)(2/4)+(2/5)(1/4))

= 0.3/(0.3+0.1)

= 0.3 / 0.4

= 0.75