Find the probability that at least two of the men meet. It's about probability. Three men A,B and C agree to meet at a cinema. A cannot remember if it is the Cathay or Golden Screens cinema, and tosses a fair coin to decide. B also tosses a fair coin to decide whether to go to the Golden Screens or Rex. C tosses a coin to decide if he should go to Cathay or not, and in the latter case, he would toss a coin again to choose between Golden Screens and Rex.
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briefcaseTeacher (K-12)
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Draw a tree diagram with the (weighted) possibilities:
A -- .5 -- Cathay
-- .5 -- Golden
B -- .5 -- Golden
-- .5 -- Rex
C -- .5 -- Cathay
-- .5 -- None
-- .5 -- Golden
-- .5 -- Rex
One approach is to find when none meet, and take that probability from 1 (the complement):
A (Cathay) B(Golden) C(Rex) ==> (.5)(.5)(.25)=.0625
A(Cathay) B(Rex) C(Golden) ==> (.5)(.5)(.25)=.0625
A(Golden) B(Rex) C(Cathay) ==> (.5)(.5)(.5)=.125
Total=.25
Since the probability that none will meet is .25, the probability that at least two will meet is .75
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Another approach is to find that there are 12 possibilities: 2 choices for A, 2 choices for B, and 3 choices for C thus 2*2*3=12.
In three of those choices no one meets, so in 9 choices at least two meet.
The possibilities:
AC AC AC AC AC AC AG AG AG AG AG AG
BG BG BG BR BR BR BG BG BG BR BR BR
CC CG CR CC CG CR CC CG CR CC CG CR
2C 2G x 2C x 2R 2G 3G 2G x 2G 2R
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