F3 Maths (-_-'')

2008-11-30 10:50 pm
Draw a tree diagram to answer the question.

A bag contains 2 red cards and 2 white cards. 2 cards are taken out of the bag one by one without replacement.

Find the probability that

(i) both cards are of the same colour,

(ii) the two cards are of different colours.
更新1:

Draw a tree diagram plz!

更新2:

001 correct, but no tree diagram. 002 wrong.

回答 (3)

2008-12-01 5:39 am
✔ 最佳答案
       (1/3)2nd=red             
       /             
 (2/4)1st=red  \                  
 /      (2/3)2nd=white             
 \       (2/3)2nd=red            
 (2/4)1st=white  /                  
        \            
        (1/3)2nd=white
(i) p(same color)
= p(1st red & 2nd red) + p(1st white & 2nd white)
= p(1st red) x p(2nd red) + p(1st white) x p(2nd white)
= 2/4 x 1/3 + 2/4 x 1/3
= 1/3

(ii) p(diff color)
= p(1st red & 2nd white) + p(1st red & 2nd white)
= p(1st red) x p(2nd white) + p(1st red) x p(2nd white)
= 2/4 x 2/3 + 2/4 x 2/3
= 2/3

2008-11-30 21:41:31 補充:
I am sorry I don't know how to draw well here
if you need to refer to the diagram format
you may read your text book or visit here:
http://www.regentsprep.org/Regents/math/tree/Ltree.htm

2008-11-30 21:42:39 補充:
(2/4)1st=red means
[1st=red] is the event
[2/4] is the probrability of the event
2008-11-30 11:28 pm
r=red
w=white
all possible outcomes=rr,rw,wr,ww
(i)=1/2(rr,ww)
(ii)=1/2(rw,wr)
2008-11-30 10:56 pm
(i) 1/3
(ii) 2/3

hope i helped. =]


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