MATH PROBABILITY

Question

You randomly choose one of the tiles. Without replacing the first tile, you choose a second tile. Find the probability of choosing two odd numbers.

Answer 1

if the tiles are half with odd numbers and half with even numbers

the probability of getting 2 odd tiles, randomly selected = Pr(2 odd) = (1/2(1/2) = 1/4 = .25 = 25%

that is a close approximation which assumes a very large number of tiles

with just 2 tiles, 1 even 1 odd Pr(2 odd) = 0

with 3 tiles 2 even 1 odd Pr(2 odd) = 0

with 3 tiles 1 even 2 odd Pr(2 odd) = (2/3)(1/2) = 1/3

with 4 tiles half odd Pr(2 odd) = (2/4)(1/3) = 1/6

with 5 tiles 3 even, 2 odd Pr(2odd) = (2/5)(1/4) = 1/10

with 5 tiles 3 odd, 2 even Pr(2odd) = 3/5)(2/4) = 3/20

with n tiles and p odd, Pr(2 odd)

= (p/n)(p-1)/(n-1))

= p(p-1)/n(n-1)

= (p^2-p)/(n^2 -n)

with 100 tiles, 60 odd

Pr(2 odd)

= (60/100)(59/99)

=about .3576

= 35.76%