For the given pair of events a and b, complete parts (a) and (b) below.

a. when a baby is born, it is a girl.
b. when a 16-sided die is rolled, the outcome is 1.

a. determine whether events a and b are independent or dependent. (if two events are technically dependent but can be treated as if they are independent according to the 5% guideline, consider them to be independent.)
b. find p(a and b), the probability that events a and b both occur.

(a) Option A. independent

(b)

Step-by-step explanation:

Two events A and B are considered dependent if the occurrence of one affects the probability of occurrence of another.

In this case, the events are independent because the birth of a girl or a boy does not affect the probability of obtaining a 1 by throwing a 16-sided die.

In the same way, throwing a die and obtaining the number 1 does not affect the probability that a baby is a girl or a boy.

When two events are independent then

The probability that a baby is a girl is

The probability of obtaining a 1 when casting a 16-sided die is:

Then:

the first one, all those points on the line just make a strait line.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1