# GATE | Gate IT 2005 | Question 74

In a communication network, a packet of length L bits takes link L1 with a probability of p1or link L2 with a probability of p2. Link L1 and L2 have bit error probability of b1 and b2respectively. The probability that the packet will be received without error via either L1 or L2 is

(A) (1 – b1)Lp1 + (1 – b2)Lp2
(B) [1 – (b1 + b2)L]p1p2
(C) (1 – b1)L (1 – b2)Lp1p2
(D) 1 – (b1Lp1 + b2Lp2)

Explanation:
Number of bits in a packet = L bits

Probability of link ‘l1’ = p1
Bit error probability for link ‘l1’ = b1
No bit error probability for link ‘l1’ = (1 – b1)

Probability of link ‘l2’ = p2
Bit error probability for link ‘l2’ = b2
No bit error probability for link ‘l2’ = (1 – b2)

Link ‘l1’ and ‘l2’ are mutually exclusive.
Thus, probability that the packet will be received without error = (1 – b1)Lp1 + (1 – b2)Lp2

Thus, option (A) is correct.

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