Numbers: Each row and column has a string of values from 1 to 7. There are no repeated values in any of the rows or columns. This means that there is a 1 in 7 chance of winning. Let's say you picked the value "3". There is one three in the first row, then another three in the second, and so on, until you count up exactly 7 "three"s. The same can be said if you work along the columns instead of the rows. The probability 1/7 is equal to the decimal value 0.1429 roughly which converts to 14.29%. Keep in mind that each toss is independent of the previous one.
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Ring Toss: There are 12 white bottles out of 36 bottles. Assuming each bottle is equally likely to land on, the probability of getting a white bottle is 12/36 = 1/3 = 0.333 = 33.3% roughly. Note: this is assuming that each toss lands on a bottle and there are no tosses that miss.
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Spinner: There are 8 spaces. Of these spaces, there are 3 spaces we want to land on: 1, 2, or 5. So the probability of winning is 3/8 = 0.375 = 37.5%
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Nine Sided Dice: We want either the value 2 or a number less than 4 (1,2,3). So there are 3 outcomes we want (1,2,3) out of 9 total. The probability of winning is 3/9 = 1/3 = 0.333 = 33.3% roughly which is the same chances of winning as the ring toss
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In summary, the best game to play is the spinner game because this provides the highest probability of winning (which was 37.5%)