Question

A bowl contains 5 blue balls, 3 red balls and 2 green balls. If two balls are drawn successively at random without replacement, what is the probability of:
(a) drawing a red ball on each of the two draws?
(b) drawing a red ball on the second draw?
(c) drawing a red ball on at least one of the two draws?
(d) red on the first draw and blue on the second draw?
(e) blue on the first draw given that red on the second draw?

Answer 1

a)P( drawing a red ball on each of the two draws )=(3/10)*(2/9)=1/15

b) P( drawing a red ball on the second draw )=3/10

c)P( drawing a red ball on at least one of the two draws ) =1-P(no red on both draws) =1-(7/10)*(6/9)=8/15

d)P( red on the first draw and blue on the second draw )=(3/10)*(5/9)=1/6

e) P( blue on the first draw given that red on the second draw )=P(blue on first and red on 2nd)/P(red on 2nd)

=(5/10)*(3/9)/(3/10)=5/9