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A probability provides a quantitative description of the likely occurrence of a particular event.

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conditional probability: survivial probability of patient in stage 2 given patient survived ...

p({t^{b}_{2})}$ be the pdf of time spent in stage B / stage 2 before death and this is independent of time spent in stage A let $p(t^{d})$ be the convolution of $p(t^{a})$ and $p(t^{b})$ that gives probability … From here on notation P refers to probability (& not pdf): I further calculated probability of atleast total 'T' months (a constant) till death given stage 1 already happened should be $P(\frac{t>T}{t …
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Probability of getting a run of r heads in n coin tosses where run ends at nth coin toss

This is probability $q f_{n-1}$ If first toss is head, then a tail happens and thereafter its equivalent to getting run in next n-2 coin tosses. This is probability $p q f_{n-2}$ and so on.. … Here i am referring $s_{n-3}$ to a pattern of heads and tails that's included and counted towards probability $f_{n-3}$ …
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Probability of getting a run of r heads in n coin tosses where run ends at nth coin toss

Infact the summation is of mutually exclusive and exhaustive series that results in overall probability of $f_{n}$. …
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