A biased coin gives a head with probability 0.3. It is tossed independently until a head appears. The probability that the first head occurs on toss five is ________.
The event requires four tails followed by one head. Independence lets their probabilities multiply.
Each tail has probability 0.7, so the required probability is $(0.7)^4(0.3)=$ **0.07203**, within the official 0.07–0.08 interval. No binomial coefficient is needed because the order is fixed.
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