Question

Suppose a certain rare Pokémon has a 2% chance to appear in a random battle in a certain region. (Assume the probability is the same for any given battle, independently of the others.)

a. The player will have to enter around ____ battles until encountering the rare Pokémon.

b. What is the probability the player will have to enter at least 20 battles to encounter the rare Pokémon?

c. What is the probability the player will have to enter no more than 30 battles to encounter the rare Pokémon?

d. What is the probability the player will have to enter at least 25 battles, but no more than 40 battles, to encounter the rare Pokémon?

Answer 1

a) The player will have to enter around 1/0.02 =50 battles until encountering the rare Pokémon.

b)

probability the player will have to enter at least 20 battles to encounter the rare Pokémon =P(no rare Pokémon in first 19 )

=0.98¹⁹ =0.6812

c) probability the player will have to enter no more than 30 battles to encounter the rare Pokémon

=1-P(no rare Pokémon in first 30 ) =1-0.98^30. =0.4545

d)

probability the player will have to enter at least 25 battles, but no more than 40 battles, to encounter the rare Pokémon

=

(0.98²⁴)-(0.98⁴⁰) =0.1700