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Update ProbabilityParadox.ipynb

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Fixed \$ problem
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Peter Norvig
2024-01-16 19:56:46 -08:00
committed by GitHub
parent 42f497d097
commit b8920c1bc7
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ipynb/ProbabilityParadox.ipynb
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@@ -2041,7 +2041,7 @@
"\n",
"> *A casino offers a game of chance for a single player in which a fair coin is tossed at each stage. The pot starts at 2 dollars and is doubled every time a head appears. The first time a tail appears, the game ends and the player wins whatever is in the pot. Thus the player wins 2 dollars if a tail appears on the first toss, 4 dollars if a head appears on the first toss and a tail on the second, etc. What is the expected value of this game to the player?*\n",
"\n",
"To calculate the expected value, we see there is a 1/2 chance of a tail on the first toss (yielding a pot of $2) and if not that, a 1/2 × 1/2 = 1/4 chance of a tail on the second toss (yielding a pot of $4), and so on. So in total, the expected value is:\n",
"To calculate the expected value, we see there is a 1/2 chance of a tail on the first toss (yielding a pot of 2 dollars) and if not that, a 1/2 × 1/2 = 1/4 chance of a tail on the second toss (yielding a pot of 4 dollars), and so on. So in total, the expected value is:\n",
"\n",
" 2 * (1/2) + 4 * (1/4) + 8 * (1/8) + ... = 1 + 1 + 1 + ... = ∞\n",
"\n",