Solution Found!
A supermarket has two customers waiting to pay for their
Chapter 5, Problem 68E(choose chapter or problem)
Problem 68E
A supermarket has two customers waiting to pay for their purchases at counter I and one customer waiting to pay at counter II. Let Y1 and Y2 denote the numbers of customers who spend more than $50 on groceries at the respective counters. Suppose that Y1 and Y2 are independent binomial random variables, with the probability that a customer at counter I will spend more than $50 equal to .2 and the probability that a customer at counter II will spend more than $50 equal to .3. Find the
a joint probability distribution for Y1 and Y2.
b probability that not more than one of the three customers will spend more than $50.
Questions & Answers
QUESTION:
Problem 68E
A supermarket has two customers waiting to pay for their purchases at counter I and one customer waiting to pay at counter II. Let Y1 and Y2 denote the numbers of customers who spend more than $50 on groceries at the respective counters. Suppose that Y1 and Y2 are independent binomial random variables, with the probability that a customer at counter I will spend more than $50 equal to .2 and the probability that a customer at counter II will spend more than $50 equal to .3. Find the
a joint probability distribution for Y1 and Y2.
b probability that not more than one of the three customers will spend more than $50.
ANSWER:
Solution:
Step 1 of 2:
Let and
denote the numbers of customers who spend more than $50 on groceries at the respective counters (I and II).
and
are independent binomial random variables.
The probability that a customer at counter I will spend more than $50 equal to 0.2.
The probability that a customer at Counter II will spend more than $50 equal to 0.3.
We have to find
- The joint probability distribution for Y1 and Y2.
- The probability that not more than one of the three customers will spend more than $50.