Posted by **maria** on Thursday, November 24, 2011 at 6:55am.

Select numbers a and b between 0 and 1

independently and at random, and let c be their sum. Let A, B, and C be the results when a, b, and c, respectively, are rounded to the nearest integer. What is the probability that A + B = C?

- Probability Pțease helpp -
**Reiny**, Thursday, November 24, 2011 at 10:58am
If a and b are decimals between 0 and 1, then

A and B could be either 0 or 1

The prob of a rounded up to 1 is 1/2 and

the prob of a becoming 0 is 1/2

forming a table:

A B -----C

0 0 ----- 0 e.g. .2+.1 = .3 --> 0

0 0 ----- 1 e.g. .4 + .4 = .8 ---> 1 ...... FALSE

0 1 ----- 1 e.g. .4 + .9 = 1.3 ---> 1

1 0 ----- 1 e.g. .9+.4 = 1.3 --> 1

1 1 ----- 1 e.g. .6 + .6 = 1.2 ---> 1 ... FALSE

1 1 ----- 2 e.g. .9+.9 = 1.8 ---> 2

I see 4 cases out of the 6 where A+B = C

so prob = 4/6 = 2/3

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