Consider two events such that p(a) = 1/4 , p(b) = 2/3 , and p(a ∩ b) = 1/5 . are events a and b independent events? yes, they are independent because p(a) ⋅ p(b) = p(a ∩ b) no, they are dependent because p(a) ⋅ p(b) = p(a ∩ b) yes, they are independent because p(a) ⋅ p(b) ≠ p(a ∩ b) no, they are dependent because p(a) ⋅ p(b) ≠ p(a ∩ b)

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1