Question

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.

Answer 1

(a) Option A. independent

(b)
`P(A\ and\ B) = 0.0312`

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

`P(A\ and\ B) = P(A)*P(B)`

The probability that a baby is a girl is

`P(A) = 0.5`

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

`P(B) = (1)/(16)`

Then:

`P(A\ and\ B) = 0.5 * (1)/(16)`

`P(A\ and\ B) = 0.0312`