Winning A Lottery: Probability and Co-incidence

a few days ago, a women in glasgow won a lottery worth more than £ 35 millions (approximately rm 245 millions), the UK biggest ever lottery payout . on 4th august, mark page won £ 4.7 millions. 3 persons won in july with prizes worth £ 6 millions in total. at first, i was quite shocked because i never thought people will win lottery that often. i thought maybe there will be a couple of winners a year. but, i was wrong. this is my motivation to comment about this issue.

i'll use lotto for an example. the rule is very simple, choose 6 numbers between 1-49. if you get all 6 numbers correct and in the right order, you won the first prize, 5 numbers correct for 2nd prize and so on until the fifth prize.

first, lets analyse the chances of winning a lottery in mathematical point of view. there are 49 possibilities of the first number being drawn, 48 possibilities for the second number and so on. so, if we multiply the numbers 49 x 48 x 47 x 46 x 45 x 44, we get 10,068,347,520. however, each possible group of six numbers (combination) can be drawn in different ways depending on which number in the group was drawn first, which was drawn second, and so on. there are 6 choices for the first, 5 for the second and so on. multiply these numbers 6 x 5 x 4 x 3 x 2 x 1 = 720. then, divide 10,068,347,520 by 720 and we will get 13,983,816. therefore, the probability is 1/13,983,816 = 0.00000007151. This is roughly the same probability as obtaining 24 heads in succession when flipping a fair coin (almost impossible isn't it). the probability of winning a lottery first prize is 0.00000007151 or 1 in 14 millions. the chances of winning is infinitesimal.

but why lots of people still playing this games? because lots of people attracted with the huge amount of money they could win and the stake is low (a pound for each combination). people don't really think about the chances of winning the lottery. usually, people tend to overestimate the chance of something good happening to them even if the odds are infinitesimal whereas people often underestimate the chance of something bad occurring. for example, if you were told by a doctor that you have a one in fourteen million chance of getting cancer in the next seven days, people will say 'oh well it is obviously not going to happen to me it is so infinitesimal'. but, the fact that there is a one in fourteen million chance of winning the lottery people think 'yes, it's got to be someone, why can't it be me.

according to psychologist, the so called 'near miss' is also a factor that makes people want to play again. if your number is 17, and the number 18 is drawn, people will think, "i was so close...". even if number 27 is drawn, some people will intrepret it as near miss.

besides, a lot of people also do not understand the odds of the lottery. In a recent survey, 21% of people thought that if they put the same numbers on to the lottery for the rest of their lives that they would have a chance of winning. This is totally wrong. They don't understand that each number retains the same chance of winning no matter how many draws take place. the chances of winning is 1 in 14 million. however, some people also does not understand how big is 14 million.

the probability of winning is very slim. but why lots of people win the lottery? this is because lots of people play the games. the population of UK is approximately 60 millions. if 14 millions (23 %)of people play the lottery for the same draw and each of them choose different combination, of course there will be a person who gonna win. but in reality, this is almost impossible to happen. the chances of people in the UK to win is realistic, but the chances of YOU winning the lottery is very very slim.

is it wise to spend your money for lottery? in fact, lottery is a type of gambling and therefore it is forbidden in Islam. so, think wisely before you play.