Probability (30 questions)

For each event, compute its probability p and the corresponding bet payout round(1000 * p / (1 - p)) (Kelly-style fair odds for a 1000-unit stake).

def bet(p: float) -> int:
 return round(1000 * p / (1 - p))

#	Question	Probability	Bet
1	Draw one card, face card (J,Q,K)	12/52	300
2	20 marbles (11G/9B), draw 1 green	11/20	1222
3	Random hour in day, hour [9, 17)	8/24	500
4	Flip 2 coins, HH	1/4	333
5	Roll 6-sided die, NOT a 6	5/6	5000
6	Spinner 1–10 twice, sum = 15	6/100	64
7	Flip 4 coins, at least one head	15/16	15000
8	Flip 2 coins, at least one head	3/4	3000
9	Random 4-digit number, last two = 00	1/100	10
10	Roll 2 dice, sum = 12	1/36	29
11	Wheel 9 sections, lands on 1–5	5/9	1250
12	Random day in Feb 2025, weekday	20/28	2500
13	Random int 1–20, prime	8/20	667
14	Roll fair die, odd	1/2	1000
15	Single card, Ace	4/52	83
16	Flip 2 coins, sequence HT	1/4	333
17	Flip fair coin, heads	1/2	1000
18	Digit 0–9, odd	5/10	1000
19	Random day in August, prime	11/31	550
20	Random int 1–100 divisible by 15	6/100	64
21	Random letter, vowel (A,E,I,O,U)	5/26	238
22	Flip 3 coins, exactly 2 heads	3/8	600
23	Random day of week, weekday	5/7	2500
24	Roll 11-sided die, 1–7	7/11	1750
25	Random month = birth month	1/12	91
26	Random int 1–20 divisible by 4	5/20	333
27	Random int 1–20 NOT divisible by 4	15/20	3000
28	Last phone digit = 7	1/10	111
29	Widget NOT failure (98% pass)	49/50	49000
30	Random month, NOT birth month	11/12	11000