without replacement

Question

Three balls are selected at random WITHOUT replacement from an urn with 5 WHITE and 4 BLUE balls. Calculate the probability that:

 

a) two balls will be white and 1 ball will be blue

 

b) All three will be the same color

 

c) EXACTLY two of the balls will be of one color

Answer 1

Three balls are selected at random WITHOUT replacement from an urn with 5 WHITE and 4 BLUE balls. Calculate the probability that:

a) two balls will be white and 1 ball will be blue

 

Draw

wbw=5/9(4/8)(4/7)=10/63

wwb=5/9(4/8)(4/7)=10/63

bww=4/9(5/8)(4/7)=10/63

 

Pof2white=10/21

 

b) All three will be the same color

 

www=5/9(4/8)(3/7)=5/42

bbb=4/9(3/8)(2/7)=2/42

 

p3same=5/42+2/42=7/42=1/6

c) EXACTLY two of the balls will be of one color

 

the 10/21 from part a For 2 whites 

plus

bbw=4/9(3/8)(5/7)=5/42

bwb=4/9(5/8)(3/7)=5/42

wbb=5/9(4/8)(3/7)=5/42

 

10/21+5/14

(20+15)/42

p2same=35/42=5/6