题目
A coin is biased so that the probability of obtaining a head when it is thrown is 0.4. The coin is thrown repeatedly until the first head is obtained.
(a) Find the probability that the first head is obtained on the 5th throw.
(b) Find the probability that the first head is obtained after the 6th throw.
题目中文翻译
一枚不均匀硬币每次抛掷时出现正面的概率为 0.4。反复抛掷这枚硬币，直到首次出现正面为止。
(a) 求第 5 次抛掷时首次出现正面的概率。
(b) 求第 6 次抛掷之后才首次出现正面的概率。
原卷通用作答要求
Answer all questions. You should use a calculator where appropriate.
You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator.
Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.
请回答所有题目。适当时应使用计算器。必须清楚展示所有必要的计算过程；仅给出计算器答案而没有过程，不予评分。除非题目另有精度要求，非精确数值答案保留 3 位有效数字，以度为单位的角度保留 1 位小数。
解答
(a)
解法一
思路
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首次正面在第5次，要求前4次都是反面，第5次为正面。
答题过程
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(b)
解法一
思路
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第6次之后才首次出现正面，等价于前6次全是反面，不必限制第7次的结果。