A box contains 4 tickets: red ticket #1, red ticket #2, green ticket #1 and green ticket #2. Two tickets are drawn from the box without replacement.
a. Find the probability that both tickets chosen are red given that at least one of them is red.

b. Find the probability that both tickets chosen are red given that at least one of them is red ticket #1.

Question

A box contains 4 tickets: red ticket #1, red ticket #2, green ticket #1 and green ticket #2. Two tickets are drawn from the box without replacement. 
a.    Find the probability that both tickets chosen are red given that at least one of them is red.

b.    Find the probability that both tickets chosen are red given that at least one of them is red ticket #1.

anonymous · Answer

a) There are 3 situations that fit this description: P(RR), P(RG), P(GR). Each of them has equal probability. (whether they're ticket #1 or #2 doesn't matter here)

b) This is similar to the situation above, except that now you discard all scenarios that don't have red ticket #1 in them: $P(R_1R_2), P(R_1G_1),P(R_1G_2),P(R_2R_1),P(G_1R_1),P(G_2R_1)$

anonymous · Answer

R=Red Ticket #1
r=Red Ticket #2
G=Green Ticket #1
g=Green Ticket #2

              matches requirements 
Draws   of question
------ ---------------------
RR         a, b
Rr          a, b
RG
Rg
rR          a, b
rr           a
rG
rg
GR
Gr
GG
Gg
gR
gr
gG
gg


a)  P=4/16
b)  P=3/16

anonymous · Answer

Thank you all for your explanations. I really appreciate it!