According to records from 50 years, there is a 2/3 chance of June temperatures being above 80 F. Azul needs to find the probability that it will be above 80 F for 20 or more days this June. There are 30 days in June. If we use a number cube with the numbers 1-6 and assign 1-4 as a temperature above 80 F and 5-6 as a temperature 80 F or below, what is the best way to peform the simulation?

Answer:Probability that temperature goes above 80 F =P= Success = [tex]\frac{2}{3}[/tex]Probability that the temperature goes below 80 F or 80 F =Q= Not Success= [tex]1-\frac{2}{3} =\frac{1}{3}[/tex]Number of Days in June = 30 DaysProbability ,that it will be above 80 F for 20 or more days this June      =   [tex]_{20}^{30}\textrm{C}P^{20}Q^{10}+_{21}^{30}\textrm{C}P^{21}Q^{9}+_{22}^{30}\textrm{C}P^{22}Q^{8}+_{23}^{30}\textrm{C}P^{23}Q^{7}+.........+_{30}^{30}\textrm{C}P^{30}Q^{0}[/tex]The best way to perform stimulation if we use a number cube with the numbers 1-6 and assign 1-4 as a temperature above 80 F and 5-6 as a temperature 80 F or below, Shows that we have marked four numbers i.e (1-4) as temperature above 80 F , so maximum number of days in june are of temperature above 80 F and less number of days are of the temperature, which is below 80 F or equal to 80 F.By converting it into a cube then playing the game in classroom by collecting money from classmates by making five groups and rolling cube five times  , if number from (1-4) comes after rolling the cube you will win $5 money and if number from (5-6) comes you win $10.The group who has maximum correct answer wins the game.