Question

Julie is taking two books with her on vacation. Suppose the probability she likes the first book is 0.5, the probability she likes the second book is 0.4, and the probability she likes both books is 0.3.
a. What is the probability she likes at least one of the books?
b. What is the probability she likes neither of the books?

Answer 1

Answer:

a. 0.6

b. 0.4

Step-by-step explanation:

Let's call

B1: she likes the first book

B2: she likes the second book

Then, P(B1) = 0.5, P(B2) = 0.4 and P(B1∩B2) = 0.3

a. she likes at least one of the books = P(B1∪B2) = P(B1) + P(B2) - P(B1∩B2)  = 0.6

b. she likes neither of the books = she doesn't like at least one of the books = 1 - P(B1∪B2) = 0.4

Answer 2

Using Venn probabilities, it is found that there is a:

a) 0.6 = 60% probability she likes at least one of the books.

b) 0.4 = 40% probability she likes neither of the books.

This question is solved using Venn probabilities, and we are going to say that:

• Event A: Represents liking the first book.
• Event B: Represents liking the second book.

The probabilities given are: $P(A) = 0.5, P(B) = 0.4, P(A \cap B) = 0.3$.

Item a:

This probability is:

$P(A \cup B) = P(A) + P(B) - P(A \cap B)$

Then

$P(A \cup B) = 0.5 + 0.4 - 0.3 = 0.6$

0.6 = 60% probability she likes at least one of the books.

Item b:

This probability is:

$p = 1 - P(A \cup B) = 1 - 0.6 = 0.4$.

0.4 = 40% probability she likes neither of the books.

A similar problem is given at https://brainly.com/question/13219828