Is there any who can show how to calculate the cumulative probability of something occurring when multiple probabilities are involved?
I am aware of how to calculate the binomial distribution for probabilities that are constant but not when they vary. For example, if a fair coin was flipped 4 times and I was making a guess each time, the probability of me guessing wrong at least:
4 times is 6.25% or 1 in 16 experiments
3 or more times is 31.25% or 5 in 16 experiments
2 or more times is 68.75% or 11 in 16 experiments
1 or more times 93.75% or 15 in 16 experiments
0 or more times is 100% or 16 in 16 experiments
So, here are some relevant probabilities (actually they are real NHL ML numbers) and there outcomes (1=win, 0=lose):
-111 1
-143 1
-125 0
-135 1
-112 1
-109 1
-107 0
-110 0
-111 1
-116 1
-106 0
-120 1
-110 1
-123 0
-124 1
-118 0
-135 0
-109 0
175 0
216 0
184 0
179 1
150 0
265 0
189 0
185 0
144 1
145 0
152 0
188 0
145 0
185 0
175 1
212 1
178 1
167 1
192 0
180 0
153 1
168 0
180 1
307 1
175 1
170 0
200 1
175 1
236 0
157 0
188 0
222 0
270 1
147 1
164 1
172 1
183 1
Assuming a bet to win an equal percentage of bankroll for each of the above events, my results would be:
Win 48.332811 units, Bet 41.766906 units for a net ROI of 15.7%.
2 questions:
1) What was the probability that I would win "at least" the 15.7% that was obtained during this experiment and how is that calculated?
2) How do you calculate the probability of winning or losing various ROI amounts? (e.g. win 2%, 5%, 10%, etc.)
There are bonus smiley faces etc. if Excel type formulas are included with math notations answers.