Final answer:
The probability that it takes 5 flips for the first head to occur on a weighted coin can be calculated using geometric distribution formula, resulting in a probability of 0.042.
Explanation:
The probability that it takes 5 flips for the first head to occur can be calculated using geometric distribution.
In this case, the probability of success (getting a head) is 0.647, and the probability of failure (getting a tail) is 1 - 0.647 = 0.353.
The probability that the first head occurs on the 5th flip is given by (0.353)^4 * 0.647 = 0.042 (rounded to three decimals).
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