A local bank reports that 70% of its customers maintain a chequing acct, 50% have a savings acct and 40% have both.If a customer was chosen at random
a) what is the probability customer has a chequing or saving acct
b)probability the selected customer has neither
c)probability the customer has a chequing but no savings
d) probability the customer has exactly one of the two types of accounts?
sorry, these are all percentages
No problem! I can help you with that. To solve these probability questions, we will need to use some basic principles of probability and set theory.
Let's assume that there are 100 customers in total (we choose 100 as it is easier to work with percentages). From the given information, we can determine the following:
a) To find the probability that a customer has a chequing or savings account, we need to add the probabilities of having a chequing account and a savings account, and then subtract the probability of having both:
Probability (Chequing or Savings) = Probability (Chequing) + Probability (Savings) - Probability (Both Chequing and Savings)
Probability (Chequing or Savings) = 70% + 50% - 40% = 80%
Therefore, the probability that a customer has a chequing or savings account is 80%.
b) To find the probability that the selected customer has neither a chequing nor a savings account, we can subtract the probability of having either a chequing or a savings account from 100% (since the customer must have at least one type of account):
Probability (Neither Chequing nor Savings) = 100% - Probability (Chequing or Savings)
Probability (Neither Chequing nor Savings) = 100% - 80% = 20%
Therefore, the probability that a customer has neither a chequing nor a savings account is 20%.
c) To find the probability that the customer has a chequing account but no savings account, we subtract the probability of having both accounts from the probability of having a chequing account:
Probability (Chequing but No Savings) = Probability (Chequing) - Probability (Both Chequing and Savings)
Probability (Chequing but No Savings) = 70% - 40% = 30%
Therefore, the probability that a customer has a chequing account but no savings account is 30%.
d) To find the probability that the customer has exactly one of the two account types (either a chequing or a savings account but not both), we need to subtract the probability of having both accounts from the probability of having either a chequing or a savings account:
Probability (Exactly One of the Two Accounts) = Probability (Chequing or Savings) - Probability (Both Chequing and Savings)
Probability (Exactly One of the Two Accounts) = 80% - 40% = 40%
Therefore, the probability that a customer has exactly one of the two types of accounts is 40%.