Consider a situation in which p(x) = 4/5 and p(y) = 1/4. if p(x and y) is = 1/5, which best describes the events?
they are independent because p(x) x p(y) = p(x and y).
they are independent because p(x) + p(y) = p(x and y).
they are dependent because p(x) x p(y) = p(x and y).
they are dependent because p(x) + p(y) = p(x and y).

 The correct option is

(A)

Step-by-step explanation:  We are given to consider a situation in which X and Y are two events such that

We are to select the statement that best describes the events X and Y.

We know that

any two events A and B are said to be independent if

We have, for events X and Y,

Thus, X and Y are independent because

Option (A) is CORRECT.

29 mil

step-by-step explanation:

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560