# 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.

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...

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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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