Let's assume we have two types of unfair coins. One has $70\%$ probability of getting head, and the other has $70\%$ change of getting tail. Now if we throw coin A $k$ times and coin B $n$ times. What will be the probability of getting at least $w$ heads. $w < k+n.$ I have it figured out when it comes to one coin. By using Normal distribution (aproximating Binomial distribution). But things get too complicated with second coin. Could you help me out?
2026-04-12 20:51:56.1776027116
Two types of coins are being tossed
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Let $X$ be the number of heads for coin $A$, and $Y$ the number for coin $B$. $X$ is approximately distributed like $N(0.7k, 0.21k)$, while $Y$ is approximately $N(0.3n, 0.21n)$. This means that $X+Y$ is approximately $$ N(0.7k+0.3n,0.21(k+n)), $$ so you can use a normal distribution with these parameters to approximate $X+Y$.