Emmanuel Pace

2022-07-19

In the Florida lottery game, you select six numbers from a pool of numbers from 1 to 53 (see flalottery.com). Each wager costs \$1. You win the jackpot if you match all six numbers that you have selected (Questions f to i are optional. Questions f to i will not be graded). Find the probability of a) Wining the jackpot. b) Matching five numbers. c) Matching four numbers. d) Matching three numbers. e) Matching two numbers.

Sheldon Castillo

a)
P( Wining the jackpot) =P(match 6 out of 6 winning numbers) $=\frac{C\left(6,6\right)}{C\left(53,6\right)}\phantom{\rule{0ex}{0ex}}=\frac{1}{22957480}$
b)
P( Matching five from 6 numbers and 1 from 47 remaining) = $C\left(6,5\right)\cdot \frac{C\left(47,1\right)}{C\left(53,6\right)}\phantom{\rule{0ex}{0ex}}=6\cdot \frac{47}{22957480}\phantom{\rule{0ex}{0ex}}=\frac{2}{162819}$
c)
P(Matching four numbers)
$=C\left(6,4\right)\cdot \frac{C\left(47,2\right)}{C\left(53,6\right)}\phantom{\rule{0ex}{0ex}}=15\cdot \frac{1081}{22957480}\phantom{\rule{0ex}{0ex}}=\frac{3243}{4591496}$
d)
P(Matching three numbers)= $C\left(6,3\right)\cdot \frac{C\left(47,3\right)}{C\left(53,6\right)}\phantom{\rule{0ex}{0ex}}=20\cdot \frac{16215}{22957480}\phantom{\rule{0ex}{0ex}}=\frac{16215}{1147874}$
e)
P(Matching two numbers)= $C\left(6,2\right)\cdot \frac{C\left(47,4\right)}{C\left(53,6\right)}\phantom{\rule{0ex}{0ex}}=15\cdot \frac{178365}{22957480}\phantom{\rule{0ex}{0ex}}=\frac{535095}{4591496}$

Do you have a similar question?