Answer: [tex]\dfrac{14}{15}[/tex]
Step-by-step explanation:
Given: Total number of flasks = 6
Number of flasks contain water =2
Number of flasks contains hydrogen peroxide =4
Total 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]]
