# probability equation multiplication understanding

I want to understand this probability equation. I'll be grateful, if someone can help.

$$P(\text{Birth})P(\text{Death}) + (1-P(\text{Birth}))(1-P(\text{Death}))$$

The above is the transition probability of a birth-death process. Can any one explain, why does these multiplications and additions represent.

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Specifically, assuming that birth and death events are independent, $(1-P(\text{Birth}))(1-P(\text{Death}))$ is the probability that neither a birth nor a death occurs, i.e. that nothing happens at all, while $P(\text{Birth})P(\text{Death})$ is the probability that both a birth and a death occur during the same time step, which obviously also doesn't change the total population size. Since all the other possibilities (a birth and no death, or a death and no birth) do change the population size, the sum of the first two probabilities is the total probability that the population does not change on this time step.