Check the probability that a system is blocked by errors

Question

A system is blocked when in a sequence of 4 bit occurs more then 3 errors OR 3 consecutive errors... We know that the probability that an error occur is 0.1 now check the probability that the system can be blocked.

How can I solve this problem? Bayes or binomial approach? I haven't understand the problem and I'm newbie about this argument...Thank you very much

Answer 1

It does seem this can be read in several ways.

Blocked if a specific 4-bit packet has BBBG, GBBB or BBBB? In that case I get from R probability 0.0019.

2*.1^3*.9 + (.1)^4
[1] 0.0019

Or is it a continuous stream of bits? Then any three consecutiveBs can block. For example GGBB immediately followed by BGGG. Then, starting at a randomly chosen point, the probability of a blockage on at the next bit would depend on assumptions about the immediate past history.