Different r.v. under the Binomial dist.

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Supposing $W_1,W_2,...,W_m$ is an iid and has dist Binomial with parameters $(t,p)$.

What is the $p(t^*\neq t)$ with estimator $t^*=\max_{i=1,...,m} W_i$?

What I did: found it is equivalent in idea to $p(t^*\le k)$. I get a product of sums mess. How can I sort this?

Answer should look like $(1-p^t)^m$

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Hint: $$P(t^* \ne t) = P(t^* \le t-1) = P(W_1 \le t-1) \cdot P(W_2 \le t-1) \cdots P(W_m \le t-1).$$