Questions
Probability
Consider randomly selecting a student at a certain university, and let A denote the event that the selected individual has a Visa credit card and B be the analogous event for a MasterCard. Suppose that P(A)=0.5 , P(B)=0.4 and P(A\( \cap \)B)=0.25.
(a) Compute the probability that the selected individual has at least one of the two types of cards (i.e., the probability of the event A\( \cup \)B).
(b) What is the probability that the selected individual has neither type of card?
(c) Describe, in terms of A and B, the event that the selected student has a Visa card but not a MasterCard, and then calculate the probability of this event.
In: Statistics and Probability
probability
Determine the probability that exactly 3 of these cards are Aces.
Determine the probability that all five of these cards are Spades.
Determine the probability that exactly 3 of these cards are face cards.
Determine the probability of selecting exactly 2 Aces and exactly 2 Kings
Determine the probability of selecting exactly 1 Jack
In: Math
Probability
In a standard deck of 52 cards, a card is chosen at random. What is the probability of choosing an ace card or a black card?
In: Math
Probability
If 2 cards are drawn from a deck of cards, how do you find P(heart or club)?
In: Statistics and Probability
Probability
Suppose the diagram of an electrical system is as given in Figure. What is the probability that the system works? Assume the components fail independently.
In: Statistics and Probability
Probability.
An fair die is thrown double times. Assume that the event A is “odd number on the first throw” and B the event “odd number on the second throw”. Compare the independence of the events A and B.
In: Math
Probability.
Given that the events A and B are such that P(A) = 1/2, P (A ∪ B) = 3/5, and P(B) = p. Find p if they are
(i) mutually exclusive
(ii) independent
In: Math
Probability
5 cards are drawn successively from a well-shuffled pack of 52 cards with replacement. Determine the probability that
(i) all the five cards should be spades?
(ii) only 3 cards should be spades?
(iii) none of the cards is a spade?
In: Math
Probability
Let 𝑋 be a CRV with PDF
a. Find the value of the constant 𝑐.
b. Show that 𝜃̂ = 3𝑋̅ is an unbiased estimator for 𝜃.
c. Find the maximum likelihood estimator for 𝜃.
In: Statistics and Probability
Willow Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions...
Willow Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. On weekday mornings, arrivals to the drive-up teller window occur at random, with an arrival rate of 24 customers per hour or 0.4 customers per minute. In the same bank waiting line system, assume that the service times for the drive-up teller follow an exponential probability distribution with a service rate of 36 customers per hour, or 0.6 customers per minute. Determine the following operating characteristics for the system:
- The probability that no customers are in the system. If
required, round your answer to four decimal places.
P0 = ?? - The average number of customers waiting. If required, round
your answer to four decimal places.
Lq = ?? - The average number of customers in the system. If required,
round your answer to nearest whole number.
L = ?? - The average time a customer spends waiting. If required, round
your answer to four decimal places.
Wq = ?? min - The average time a customer spends in the system. If required,
round your answer to nearest whole number.
W = ??min - The probability that arriving customers will have to wait for
service. If required, round your answer to four decimal
places.
Pw = ??
In: Operations Management