If network would include 2 mining pools (pool_1 and pool_2) with the hashpower of 49% and 51%,respectively, then wo want to calculate the probability that in 10 minutes, exactly 2 blocks would be generated such that two blocks are not generated at the same time and the first block is generated by pool_1 with hashpower of 49% and second block is generated by pool_2 with hashpower of 51% ?
(1) It is important for us to know which pool generates the first block and which one generates the second block, so, we want to know the probability that the first block is generated by which pool (regarding to their hashpower)
(2) we assume that pool_2 is honest and pool_1 is selfish and
(3) We know that Bitcoin network on average generates one block per 10 minutes.)
(According to solution that is proposed by Murch here : How can we be sure that a new block will be found?)