Suppose there are two full bowls of cookies. bowl #1 has 10 chocolate chip and 30 plain cookies, while bowl #2 has 20 of each. our friend fred picks a bowl at random, and then picks a cookie at random. we may assume there is no reason to believe fred treats one bowl differently from another, likewise for the cookies. the cookie turns out to be a plain one. how probable is it that fred picked it out of bowl #1?

answer:

to get a plain cookie:

we could have (1,p) or (2,p)

prob (1, p)= (1//40) = 3/8

prob (2,p) = (1/2)(20/40) = 1/4

prob(plain cookie) = 3/8 + 1/4 = 5/8

(checking:

prob(1,c) = (1/2)(10/40) = 1/8

prob(2,c) = (1/2)(20/40) = 1/4

note 3/8+1/4+1/8+1/= 1 , check! )

could have stopped at

prob (1, p)= (1//40) = 3/8

step-by-step explanation:

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation: