Problem: What's the probability of winning the jackpot of the
California lottery? Note, to win the jackpot you must pick 5 numbers
from 1-47, and then pick a MEGA number from 1-27. All 5 numbers
must match the numbers chosen, and the MEGA number must match
the MEGA number chosen.
First, the easy part:
(a) The probability that you match the MEGA number is simply 1
in 27. The way the game is set up, the MEGA number is completely
separate from the other 5 numbers.
(b) The probability that you match the other 5 numbers is
The probability that you match the 5 numbers and the MEGA number,
thus winning the jackpot, is
Note: the game previously was that you had to choose 6 numbers
from 1 to 51 (with no MEGA number). That game was easier, providing
you 1 in 18,009,460 odds. (left as an exercise to the reader)
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