Lottery chances are $\frac{1}{50}$ for every bought ticket. John participates $30$ times, $10$ times he buys $4$ tickets but the other times only $1$. what are his chances at winning at least once?
Does this mean i should evaluate $(1-(1-\frac{4}{50})^{10})(1-(1-\frac{1}{50})^{20})$?
Thanks in advance!
Almost, a slight mistake:
Think about the probability of not winning $W^c$:
$$P(W^C) = P(4T^C)P(1T^C) = 1 - \left(1 - \left(\frac{4}{50}\right)^{10}\right)\left (1 - \left(\frac{1}{50}\right)^{20} \right) $$ $$P(4T^c) = 1-P(4T) = 1 - \left(\frac{4}{50}\right)^{10} $$ $$P(1T^c) = 1-P(1T) = 1 - \left(\frac{1}{50}\right)^{20} $$