ASSIGNMENT # 8: Introduction to Probability 111 (1) A department store made a st
ID: 3361834 • Letter: A
Question
ASSIGNMENT # 8: Introduction to Probability 111 (1) A department store made a study of the personal checks it received for payment of goods. It discovered that 40% of all bad checks (with insufficient funds) had the wrong date on them, while only 2% of all good checks (with sufficient funds) had the wrong date on them. It also found that 0.5% of all checks received had insufficient funds to cover them. A clerk in this store received a personal check from a customer. (a) Draw a tree diagram for the situation. (b) What is the probability that the check has insufficient funds and a wrong date? (c) The clerk found the the check had a wrong date. What is the probability that it has insufficient funds? (d) What is the probability that the check has the wrong date given that it has insufficient funds? (e) What is the probability that the check has the correct date?Explanation / Answer
Solution- Let events are A- Insuffcient funds are there.
B- Sufficient funds are there
E- Wrong date is there.
In the question - P(A) = 0.005 and P(B) = 0.995 , P(E|A) = 0.4 and P(E|B) = 0.02
P( A and E )
= P(A) * P(E|A)
= 0.4 * 0.005
= 0.002
P( Insufficient funds are there given wrong date is there )
= P(A|E)
= P(A) * P(E|A) / [ P(A) * P(E|A) + P(B) * P(E|B) ] ( using bayes theorem )
= 0.005 * 0.4 / ( 0.005 * 0.4 + 0.995 * 0.02 )
= 0.0913
P( wrong date is there given insufficient funds are there )
= P(E|A)
= 0.4
P( wrong date is there )
= P(E)
= P(A)* P(E|A) + P(B)* P(E|B)
= 0.005 * 0.4 + 0.995 * 0.02
= 0.0219
Answers
TY!