六合彩連續買5期買1注一樣數字定一期隨機買5注中頭獎機率高啲？
黃禮志Yeji
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六合彩連續5期買1注一樣數字定一期隨機買5注中頭獎機率高啲？
量角器都唔駛... 你個機會係0%... 
獨立事件黎,數學上一樣。
p:中頭獎概率
買五期一注，其中一次中：
1-（1-p)^5
同一期買五注，其中一注中：
1- （1-p)^5
p:中頭獎概率
買五期一注，其中一次中：
1-（1-p)^5
同一期買五注，其中一注中：
1- （1-p)^5
人地問中嘅機會 你答唔中嘅機會
0分
0分
自膠
前者高d 但基乎冇分別
幾
如果同一組數字買1億期，定1期買1億注隨機易中d?
Sure, let's dive into the probabilities for both scenarios:
### 1. Selecting 100,000 Numbers
In this scenario, you pick 100,000 distinct numbers from a range of 1 to 1,000,000. The probability of guessing the correct number is the ratio of the number of selected numbers to the total number of possibilities. Hence, the probability is:
\[ P_1 = \frac{100,000}{1,000,000} = 0.1 \]
So, the probability of winning by selecting 100,000 numbers is **0.1**, or **10%**.
### 2. Selecting 1 Number but Rolling 100,000 Times
In this scenario, you pick a single number and try to match it with the correct number by rolling 100,000 times. The probability of not guessing the correct number in a single roll is:
\[ P_{\text{fail}} = \frac{999,999}{1,000,000} \]
The probability of failing every single one of the 100,000 times is:
\[ P_{\text{fail all}} = \left( \frac{999,999}{1,000,000} \right)^{100,000} \]
Therefore, the probability of winning at least once is:
\[ P_2 = 1 - P_{\text{fail all}} = 1 - \left( \frac{999,999}{1,000,000} \right)^{100,000} \]
Let’s compute this:
\[ P_2 = 1 - \left(0.999999\right)^{100,000} \]
Using approximation for \(e^{-x}\), where \(x\) is very small:
\[ P_2 \approx 1 - e^{-0.1} \approx 1 - 0.9048 = 0.0952 \]
So, the probability of winning by rolling 100,000 times is approximately **0.0952**, or **9.52%**.
### Summary
- **Probability of winning by selecting 100,000 numbers**: 10%
- **Probability of winning by rolling 100,000 times**: 9.52%
Interestingly, choosing 100,000 numbers offers a slightly higher probability of winning compared to rolling 100,000 times with a single number.
Which strategy would you prefer?
copilot 答案
### 1. Selecting 100,000 Numbers
In this scenario, you pick 100,000 distinct numbers from a range of 1 to 1,000,000. The probability of guessing the correct number is the ratio of the number of selected numbers to the total number of possibilities. Hence, the probability is:
\[ P_1 = \frac{100,000}{1,000,000} = 0.1 \]
So, the probability of winning by selecting 100,000 numbers is **0.1**, or **10%**.
### 2. Selecting 1 Number but Rolling 100,000 Times
In this scenario, you pick a single number and try to match it with the correct number by rolling 100,000 times. The probability of not guessing the correct number in a single roll is:
\[ P_{\text{fail}} = \frac{999,999}{1,000,000} \]
The probability of failing every single one of the 100,000 times is:
\[ P_{\text{fail all}} = \left( \frac{999,999}{1,000,000} \right)^{100,000} \]
Therefore, the probability of winning at least once is:
\[ P_2 = 1 - P_{\text{fail all}} = 1 - \left( \frac{999,999}{1,000,000} \right)^{100,000} \]
Let’s compute this:
\[ P_2 = 1 - \left(0.999999\right)^{100,000} \]
Using approximation for \(e^{-x}\), where \(x\) is very small:
\[ P_2 \approx 1 - e^{-0.1} \approx 1 - 0.9048 = 0.0952 \]
So, the probability of winning by rolling 100,000 times is approximately **0.0952**, or **9.52%**.
### Summary
- **Probability of winning by selecting 100,000 numbers**: 10%
- **Probability of winning by rolling 100,000 times**: 9.52%
Interestingly, choosing 100,000 numbers offers a slightly higher probability of winning compared to rolling 100,000 times with a single number.
Which strategy would you prefer?
copilot 答案
補返個prompt
There is a game to guess the right number from 1 to 1000000. Calculate the probabilities of winnings of 1. Selecting 100000 numbers 2. Selecting 1 number but roll for 100000 times
There is a game to guess the right number from 1 to 1000000. Calculate the probabilities of winnings of 1. Selecting 100000 numbers 2. Selecting 1 number but roll for 100000 times
全餐都只係1398萬注，你買一億做乜9
隨機可以重覆
同埋呢個係回應問題既思路
如果一樣，無論買幾多都一樣
同埋呢個係回應問題既思路
如果一樣，無論買幾多都一樣
Prompt你都未寫啱
你連六合彩規矩都冇講，仲要1000000個數字
做緊乜撚？
你連六合彩規矩都冇講，仲要1000000個數字
做緊乜撚？
唔識類比得到答案嘅話
講黎都晒氣
講黎都晒氣
我既答案係5期1注
因為可以中5次頭獎
1期5注最多只可以中1次
因為可以中5次頭獎
1期5注最多只可以中1次
咁嘅話 expectance係一樣
全餐即係一定中，機率係1。
同一組號碼買左成10年
仲未中過
仲未中過