Question

The two-way table shows the distribution of book style to genre. Miguel claims that given that the book is paperback (PB) does not affect the outcome that the book is nonfiction (NF). A 4-column table has 3 rows. The first column has entries paperback, hardcover, total. The second column is labeled Fiction with entries 20, 10, 30. The third column is labeled nonfiction with entries 60, 30, 90. The fourth column is labeled total with entries 80, 40, 120. Is Miguel’s claim correct? Yes, the two events are independent because P(NF|PB) = P(NF). Yes, the two events are independent because P(PB|NF) = P(NF). No, the two events are not independent because P(PB|NF) ≠ P(PB). No, the two events are not independent because P(PB|NF) ≠ P(NF).

Answer 1

The claim of Miguel is correct, as the two events are independent because P(NF|PB) = P(NF).

What is conditional probability?  

The conditional probability is the happening of an event, when the probability of occurring of other event is given.

$P(A|B)=\dfrac{P(A\cap B)}{P(B)}$

The probability of event A, given that the event B is occurred.

Independent events are those events whose occurrences do not depend on the other events.

The two-way table shows the distribution of book style to genre is given as,

The first column has entries paperback, hardcover, total.

The second column is labeled Fiction with entries     20,   10,   30.

The third column is labeled nonfiction with entries    60,   30,  90.

The fourth column is labeled total with entries           80,  40,  120.

Miguel claims that given that the book is paperback (PB) does not affect the outcome that the book is nonfiction (NF).

Suppose that two events are denoted by A and B. They are said to be an independent event if and only if:

$P(A \cap B) = P(A)P(B)$

Put the values as,

$\dfrac{60}{120}=\dfrac{80}{120}\times\dfrac{90}{120}\\\dfrac{1}{2}=\dfrac{1}{2}$

As both the values are equal. Thus, the claim of Miguel is correct because the two events are independent because P(NF|PB) = P(NF).

Learn more about the probability here;

brainly.com/question/24756209

Learn more about the independent events here;

brainly.com/question/12700357

Answer 2

Answer:

The correct answer is option A. :)

Step-by-step explanation:

Just got it right on edge - the above answer helped and is correct :D

Brainliest would be greatly appreciated!