Powers of ten

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Today, scientists tell us that the universe is about 10 billion years old.

10 billion years = 10,000,000,000 years = 10¹⁰ years

How many seconds are in a year?

(60 seconds/minute) * (60 minutes/hour) * (24 hours/days) * (365.25 days/year) = 31,557,600 seconds/year

Attempting an operation 300 times a second results in 10¹⁰ operations per second.

300 operations/second * 31,557,600 seconds/year = 9,467,280,000 operations/second ≈ 10,000,000,000 operations/second = 10¹⁰ operations/second

So, attempting an operation 300 times a second for 10 billion years results in 10²⁰ attempts.

10¹⁰ years * 10¹⁰ attempts/year = 10²⁰ attempts

The size of the universe is estimated at 10⁶⁶ atoms, or about 10⁸⁰ small particles (protons, neutrons, electrons, etc).

Your odds of winning the state lottery are about

1 chance in 10,000,000 = 1 chance in 10⁷.

If you buy 10 tickets (different numbers, of course), your odds improve to

1 chance in 1,000,000.

Your odds of winning two lotteries (i.e., independent tries) in a row are

1 chance in 10⁷ * 10⁷ = 1 chance in 10¹⁴

Your odds of winning three lotteries (i.e., independent tries) in a row are

1 chance in 10⁷ * 10⁷ * 10⁷ = 1 chance in 10²¹

Generalizing, your odds of winning n lotteries (i.e., independent tries) in a row are

1 chance in 10^7*n

So, the probability of

1 chance in 10^{99,999,999,890} (99,999,999,890 zeros)

is the same as winning the state lottery

99,999,999,890 / 7 = 14,285,714,270 times in a row