2) john and beth plan to visit a bookstore. based on their previous visits to this bookstore, the…

2) 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.\n\nnumber of books john will buy\n|0|1|2|3|\n|----|----|----|----|\n|.25|.30|.35|.10|\n\nnumber of books beth will buy\n|0|1|2|3|\n|----|----|----|----|\n|.20|.35|.15|.30|\n\nassuming that john and beth make their decisions to purchase books independently, what is the probability that a total of 0 books are purchased?\n\na) 0.5500\nb) 0.9500\nc) 0.0500\nd) 0.4500\ne) 0.4000

2) 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.\n\nnumber of books john will buy\n|0|1|2|3|\n|----|----|----|----|\n|.25|.30|.35|.10|\n\nnumber of books beth will buy\n|0|1|2|3|\n|----|----|----|----|\n|.20|.35|.15|.30|\n\nassuming that john and beth make their decisions to purchase books independently, what is the probability that a total of 0 books are purchased?\n\na) 0.5500\nb) 0.9500\nc) 0.0500\nd) 0.4500\ne) 0.4000

Answer

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)