A wildlife biologist examines frogs for a genetic trait he suspects may be linked to sensitivity to
industrial toxins in the environment. Previous research had established that this trait is usually
found in 1 of every 8 frogs. He collected and examines a dozen frogs. If the frequency of the
traits has not changed, what's the probability he finds the trait in no more than 4 frogs?
Solution
P = 1/8
P( 0 frog ) + P( 1 frog ) + P( 2 frog ) + P( 3 frog ) + P( 4 frog )
=( 7/8 )^12 + 12 * ( 1/8 ) * ( 7/8 )^11 + 66 * ( 1/8 )^2 * ( 7/8 )^10 + 220 *( 1/8 )^3 * ( 7/8 )^9 +
495 *( 1/8 )^4 * ( 7/8 )^8
=0.9887145218963269 = 0.9887 = 98.87%