Non Functional

From: a first course in probability by Sheldon Ross

Let's see small value of n and see if we notice a pattern ... n = 2 Education: AB The probability to be functional for two p ^ 2 n = 3 Arrangement: ABC Two pairs: AB and BC. The probability that both A and B are non-functional and functional C (1-p) ^ 2p. The probability that 4 Fitting: ABCD. Provisions of the units does not work to downgrade: AB, BC, CD, ABC, BCD, ABCD probability Final: 1 to 3 (1-p) ^ 2p ^ 2-2 (1-p) ^ 3p - 1 (1 -- p) ^ 4 n = 5 Arrangement: ABCDE provisions of units does not work to downgrade: AB, BC, CD, DE, ABC, BCD, CDE, ABCD, BCDE, ABCDE probability Final: 1 to 4 (1-p) ^ 2p ^ 3 -- 3 (1-p) 3p ^ 2-2 (1-p) ^ 4p - 1 (1-p) ^ 5 The pattern seems to be: 1 - (n-1) (1-p) ^ 2p ^ (n -2) - (N-2) (1-p) 3p ^ ^ (n-3) - (N-3) (1-p) ^ 4p ^ (n-4) - ... - (1-p) ^ n

Non Functional

Non Functional