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That first answer is wrong, it's more complicated than that, and your odds are better than 1 in 700 that you will win at least once over 4 tries.

The answer given here is incorrect.

To simplify the problem if you flip a coin once, your chances of getting heads are 50%. But if you flip a coin twice, your chances of getting at least one heads is no longer 50%. The chances go up to 75%.

This is the formula. .5 is the chance of getting your result each time. 2 is the number of times that you try it.

1 - (1 - .5)^2 = .75

All the possible combinations of flipping a coin twice are listed below. In 3 out of 4 of the combinations you got at least 1 heads. That means that 75% of the time you got at least one heads. The same principle applies to the lottery example except there are a lot more combinations.

first flip..........second flip

heads..........heads

tails..........tails

heads..........tails

tails..........heads

For the lottery example:

The chances of winning each time is 1/700 (rounds to .143% chance).

The chances of winning at least once for the year are 1 - (1 - .00143)^4 = .00571 or .571% (rounded)

The unrounded answer is 0.5702052473969179508538109119%

Actually, the way to consider this is to look at the probability of NOT winning this year and working back.

The probability of losing each lottery is 699/700, so the chance of not winning any draw is (699/700)x(699/700)x(699/700)x(699/700) - or 0.9943 in total.

As this is the chance of not winning in the year, the chance of winning is just 1 - 0.9943 = 0.0057.

Put another way, about 1 in 175 chance of winning this year.

The probability of winning at least once is the opposite of losing every time. The probability of loss in a lottery is thus 699/700.

Probability of losing 4 times in a row is 699/700*699/700*699/700*699/700.

The opposite of that is 1-699/700*699/700*699/700*699/700 =~ 0.57 % or about 1 in 175.

So in 1:175 will you win at least one in 4 lotteries.

Providing that you a ticket each of the 4 times within that year, the total probability for winning the lottery that year is 4*(1/700) = 4/700

That is simply probability of winning in the first draw or in the second draw or in the third draw or in the fourth, that is 1/700 + 1/700 + 1/700 + 1/700 = 4/700 (Addition Rule in Probability.

I can answer basic and intermediate questions. If I don`t know the answer, I`d be interested to find it for you, or to suggest somewhere you could look.

I've taught introductory statistics to college students majoring in sociology, psychology, and communications for more than a decade. However, my expertise is with respect to statistics and probability distributions for conventional statistical analyses, NOT with binomial distributions and combinatorial procedures.