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CBSE Class 10 Answered

The numbers 1≤a,b,c,d,e≤2008 are randomly chosen integers(repetition is allowed). What is the probability that abc+de is even.
Asked by acv27joy | 13 Dec, 2018, 07:44: PM
answered-by-expert Expert Answer
Let us find the probability of getting odd for (abc+de)
 
let us use the notation begin mathsize 12px style p open parentheses space x with bar on top space close parentheses end style which means probability of getting odd x and p(x) which means probability of getting even x
 
(abc+de) is odd when abc is odd and de is even   OR when abc is even and de is odd
 
probability of abc is odd and de is even = begin mathsize 12px style p open parentheses space stack a b c with bar on top space close parentheses end style×p(de) = [ begin mathsize 12px style p open parentheses space a with bar on top space close parentheses end style ×begin mathsize 12px style p open parentheses space b with bar on top space close parentheses end style ×begin mathsize 12px style p open parentheses space c with bar on top space close parentheses end style ] ×[ 1 - begin mathsize 12px style p open parentheses space d with bar on top space close parentheses end style begin mathsize 12px style p open parentheses space e with bar on top space close parentheses end style ] = [ (1/2) (1/2)(1/2) ]×[ 1 - (1/2)(1/2)] = (3/32)
probability of abc is even and de is odd = p(abc)×begin mathsize 12px style p open parentheses space stack d e with bar on top space close parentheses end style = [ 1 - begin mathsize 12px style p open parentheses space stack a b c with bar on top space close parentheses end style ]×[ begin mathsize 12px style p open parentheses space d with bar on top space close parentheses end style×begin mathsize 12px style p open parentheses space e with bar on top space close parentheses end style] = [ 1 - (1/8) ]×[(1/2)(1/2)] = (7/32)
begin mathsize 12px style p open parentheses space stack a b c plus d e with bar on top space close parentheses end style = (3/32) + (7/32) = (10/32)
Hence probability of getting even abc+de is given by,  p(abc+de) = [ 1 - begin mathsize 12px style p open parentheses space stack a b c plus d e with bar on top space close parentheses end style ]  = 1 - (10/32) = (11/16)
Answered by Thiyagarajan K | 14 Dec, 2018, 05:47: AM

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