Your science teacher sets up six flasks. Two of the flasks contain water and four of the flasks contain hydrogen peroxide. A reaction occurs when you add yeast to hydrogen peroxide. You add yeast to two of the flasks. What is the probability that at least one reaction will occur?

Answer:  [tex]\dfrac{14}{15}[/tex]Step-by-step explanation:Given:  Total number of flasks = 6Number of flasks contain water =2Number of flasks contains hydrogen peroxide =4Total outcomes :Combination of 2 flasks out of 6 :-[tex]^6C_4=\dfrac{6!}{4!(6-4)!}\ \because ^nC_r=\dfrac{n!}{(n-r)!}[/tex][tex]=\dfrac{6\times5}{2}=15[/tex]   Favorable outcomes : Combination of 2 flasks with at least one with hydrogen peroxide:[tex]^2C_1\cdot\ ^4C_1+^2C_0\cdot\ ^4C_2\ \ [\because\ ^nC_0=1,\ ^nC_1=n]\\\\=(2)(4)+(1)\dfrac{4!}{2!(4-2)!}\\\\=8+6=14[/tex]Now, the probability that at least one reaction will occur =[tex]\dfrac{14}{15}[/tex][∵ [tex]\text{Probability}=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]]