Question

1. john and beth plan to visit a bookstore. based on their previous visits to this bookstore, the probability distributions for the number of books they will buy is given below.

number of books john will buy

0	1	2	3

number of books beth will buy

0	1	2	3

assuming that john and beth make their decisions to purchase books independently, what is the probability that a total of 0 books are purchased?

a) 0.5500
b) 0.9500
c) 0.0500
d) 0.4500
e) 0.4000

Explanation:

Step1: Recall the formula for independent - event probability

If two events \(A\) and \(B\) are independent, the probability that both \(A\) and \(B\) occur is \(P(A\cap B)=P(A)\times P(B)\). We want to find the probability that the total number of books purchased is \(0\), which means John buys \(0\) books and Beth buys \(0\) books.

Step2: Identify the probabilities from the tables

Let \(P(J = 0)\) be the probability that John buys \(0\) books and \(P(B = 0)\) be the probability that Beth buys \(0\) books. From the given probability - distribution tables, \(P(J = 0)=0.25\) and \(P(B = 0)=0.20\).

Step3: Calculate the joint probability

Since John's and Beth's decisions to buy books are independent, the probability that the total number of books purchased is \(0\) is \(P=(0.25)\times(0.20)=0.0500\).

Answer:

c) \(0.0500\)