At one bank, it is known that 63% of customers have invested in a TFSA and 45% have
invested in an RRSP. Also, if a customer has invested in an RRSP, there is a 75% chance they have also
invested in a TFSA. Let T and R represent the
respectively. In each part of this question, express each
justify any computation by explicitly stating the formula you are using. Do not define additional events.
(a) Express each of the three probabilities listed above in terms of the events T and R.
(b) Are the events T and R independent? Explain.
(c) What is the probability a randomly selected customer has invested in
(i) both a TFSA and an RRSP?
(ii) a TFSA but not an RRSP?
(iii) at least one of these two types of investment products?
Trending nowThis is a popular solution!
Step by stepSolved in 5 steps with 26 images
- You want to purchase a DVD drive for your laptop computer. Assume that 55 % of the drives are made outside of the United States. Of the U.S.-made drives, 3% are defective; of the foreign-made drives, 4% are defective. If your drive is defective, find the probability that it is foreign made.arrow_forwardSuppose you play a game that you can only either win or lose. You win a game with probability 0.40. Each game you play is independent. If you play the game 10 times, What is the probability that you win 6 times out of the 10 games?arrow_forwardIn an upcoming congressional election, two democrats, Al and Bill, seek the nomination to run against the incumbent republican, George. It is estimated that George has a probability ½ of beating Al in the election if Al is the democratic nominee but only a ⅓ probability of beating Bill. Given that Al has a ⅔ probability of being the democratic nominee, what is the probability that George will be elected?arrow_forward
- The probability of rain on any day in the month of April is 34%. The probability that it will be windy on any day in the month of April is 38%, and the probability of both is 10%. What is the probability that a randomly selected day in April will be rainy or windy? The probability isarrow_forwardAn assembly line has two inspectors. The probability that the first inspector will miss a defective item is 0.03. If the defective item passes the first inspector, the probability that the second inspector will miss it is 0.07. What is the probability that a defective item will pass by both inspectors?arrow_forwardA PhD graduate has applied for a job with two universities, A and B. The graduate feels that she has a 60% chance of receiving an offer from university A, and a 30% chance of receiving an offer from university B. If she receives an offer from university B, she believes that she has an 70% chance of receiving an offer from university A. If she receives an offer from university B, what is the probability that she will not receive an offer from university A? a) 0.66. b) 0.24. c) 0.3arrow_forward
- Three airlines serve a small airport. Airline A has 55% of all scheduled flights, airline B has 33% and airline C has the remaining 12%. Their on-time rates are 85%, 64%, and 40%, respectively. A flight just left on-time. What is the probability that it was a flight of airline A?arrow_forwardMichael is playing tournament chess against a computer program and the probability he wins against the program at any given game is 0.25. Find the probability that on the given day Nigel wins for the first time on the 4th game playerarrow_forwardUnlike craps and roulette, where each throw or spin is independent of the one before it, in blackjack the probabilities for the next card depend on the cards that have been dealt so far. Since the dealer never changes his strategy, the player can overcome the house advantage by carefully counting the cards that have been dealt and betting more when his odds of winning are better. 12 face cards in total. At what points in the deal can the probability of a face card be the same as it was at the start?arrow_forward
- Two different missiles are shot simultaneously at a practice target. If the probability of the first one hitting the target is ¼ and of the second one hitting is ⅕ , what is the probability that both missiles will hit?arrow_forwardA radio device consists of 1000 electronic elements. The probability of nonoperation for one element during one year of operation is 0.001 and is independent of the condition of the other elements. What is the probability that at least two elements will fail to operate during a year?arrow_forwardDan's Diner employs three dishwashers. Al washes 20% of the dishes and breaks only 2% of those he handles. Betty and Chuck each wash 40% of the dishes, and Betty breaks only 2% of hers, but Chuck breaks 4% of the dishes he washes. You go to Dan's for supper one night and hear a dish break at the sink. What's the probability that Chuck is on the job? ... The probability that Chuck is on the job is (Round to three decimal places as needed.)arrow_forward
- A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON