Question

find the probability of winning a lottery with the following rule. select the winning four numbers from 1, 2, . . . , 29. (in any order. no repeats.)

Answer 1

The probability of winning the lottery is 0.1457 (or 14.57%)

Explanation:

Since we select 4 numbers, we have 4 chances of winning the lottery and we add these 4 chances to get the probability of winning,

There are 29 numbers, we randomly take out one,

so the probability that we have the winning number is 1/29

Now, there are 28 number left, The probability of winning for the 2nd try is then 1/28,

Then there are 27 numbers left and we get the probability, 1/27

Finally, there are 26 numbers left and the probability that our number is the winning number for the 4th try is 1/26

So the total probability is,

P = 1/29 + 1/28 + 1/27 + 1/26

P = 0.1457