You, your parents, your sister, go to visit grandma for her birthday. Grandma made a cake for the party. If she puts $20$ raisins in the cake at random in the cake, and she divides the cake into $5$ equal pieces, what's the probability that your sister gets no raisins?
Let $X$ be the number of raisins in your piece. Aside: I think $X$ is the number of raisins for each person in the family.
$X \sim Bin(n=20, \theta=1/5)$
The probability that your sister gets gets no raisins is
$P[X\in \{3,4,5,6\}]=P[X=3]+P[X=4]+P[X=5]+P[X=6]$
I don't understand the solution.
I think we should calculate $P[X=0]$ instead of $P[X\in \{3,4,5,6\}]$.
Also consider:If your sister gets no raisins, then you can at most get $8$ raisins but at least $4$ raisins. $8$ in the case where the $4$ raisins that didn't get in her slice gets into your slice and $4$ assuming someone else received her portion. Then shouldn't we calculate $P[X\in\{4,5,6,7,8,\}]$?