Some Interesting Probabilities ...
First, some definitions
Odds vs Probability:
Odds refers to the chances in favor of the event to the chances against it. It is expressed as a ratio of two
quantities, usually with a colon between the two numbers.
Probability refers to the likelihood of occurrence of an event. It is often represented as a ratio of the number of ways the
event can occur divided by the total number of possibilities,
or it can be represented by a decimal or a percentage. Probability ranges from 0 to 1, both inclusive (or 0% to 100%).
For example, if you roll one die, the odds of rolling a six would be 1 : 5 (1 way to get a six, 5 ways in which a six would not occur).
The probability of rolling a six would be 1 / 6, or .166 or 16.6% (1 chance out of 6 possibilities).
Some interesting probabilities ...
(1) The probability of a person winning the Powerball lottery is 1 out of 292,201,388.
Here is how the odds are determined:
First we will examine the rules of Powerball as it is currently configured (in 2018).
During each drawing, two drums full of balls are thoroughly mixed and randomized.
The first drum contains white balls numbered 1 to 69.
Five are drawn without replacement from this drum.
The second drum has red balls that are numbered from 1 to 26.
One of these is drawn.
The object is to match all of these numbers.
To determine all the ways in which five balls can be chosen from the 69 white balls, you need to use the combinations formula:
where n = 69 and r = 5.
Then multiply this number (11,238,513) by 26 (the number of ways the powerball can be chosen) to get 292,201,338.
So the probability of winning the Powerball Lottery is 1/292,201,338 or the odds of winning are 1 : 292,201,337.
(2) The probability of winning the Mega Millions lottery is 1 out of 302,575,350.
Players pick five numbers from 1 to 70 and a Mega number of 1 to 25.
Again, you must use the formula above to determine all the possible ways of picking five numbers out of seventy.
This time, n = 70 and r = 5.
Multiply this number (12,103,014) by 25 (the number of ways to pick the mega number) to get 302,575,350.
Therefore the probability of winning the Mega Millions lottery is 1 chance out of 302,575,350 or the odds of winning are 1 : 302,575,349.
(3) The chances of winning both the Mega Millions and the Powerball is 1 in 88 quadrillion.
The probability of winning both is 1 out of (302,575,350) x (292,201,388) or
1 out of 88,412,922,115,800,000.
(4) The probability of being audited by the I.R.S. is .04% or 1 out 250.
--
Forbes
(5) The probability of being involved in a drunk driving crash in your lifetime is 2 out of 3.
--
M.A.D.D.
(6) The probability of going blind after laser eye surgery is 1 in 5 million.
--
London Vision Clinic
(7) The probability of being injured by a toilet is 1 in 5,000.
-- The Centers for Disease Control and Prevention
(8) The probability of dying by cancer is 1 in 7.
-- The National Safety Council
(9) The probability of dying by suicide is 1 in 91.
-- The National Safety Council
(10) The probability of dying in a motor vehicle crash is 1 in 102.
-- The National Safety Council
(11) The probability of dying in an airplane crash is 1 in 205,552.
-- The National Safety Council
(12) The probability of dying after a Hornet, wasp or bee sting is 1 in 54,093.
-- The National Safety Council
(13) The probability of dying after being hit by lightning is 1 in 114,195.
-- The National Safety Council
(14) The probability of dying after choking on food is 1 in 3,138.
-- The National Safety Council
(15) The probability of getting killed by fireworks is 1 in 340,733.
-- Florida Museum
(16) The probability of dying from a shark attack is 1 in 3,748,067.
-- Florida Museum
(17) The odds of bowling a 300 game are 11,500 to 1.
-- Odds Are ...
(18) The odds of getting a hole in one are 5,000 to 1.
-- Odds Are ...
(19) The odds of being an astronaut are 13,200,000 to 1.
-- Odds Are ...
(20) The odds of winning an Olympic medal are 662,000 to 1.
-- Odds Are ...