# 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...

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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### 1 Answer

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