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For the next three problems : The probability that the San Jose Sharks will win any given game is 0.3694 based on a 13 year win history of 382 wins out of 1034 games played (as of a certain date). An upcoming monthly schedule contains 12 games.
Let
= the number of games won in that upcoming month.
The expected number of wins for that upcoming month is:
D: 4.43
What is the probability that the San Jose Sharks win 6 games in that upcoming month?
A: 0.1476
What is the probability that the San Jose Sharks win at least 5 games in that upcoming month
C: 0.4734
For the next two questions : The average number of times per week that Mrs. Plum’s cats wake her up at night because they want to play is 10. We are interested in the number of times her cats wake her up each week.
In words, the random variable =
A: The number of times Mrs. Plum's cats wake her up each week
Find the probability that her cats will wake her up no more than 5 times next week.
D: 0.0671
The next three questions refer to the following information. The Sky Train from the terminal to the rental car and long term parking center is supposed to arrive every 8 minutes. The waiting times for the train are known to follow a uniform distribution.
What is the average waiting time (in minutes)?
D
Find the 30th percentile for the waiting times (in minutes).
B
The probability of waiting more than 7 minutes given a person has waited more than 4 minutes is?
B
People visiting video rental stores often rent more than one DVD at a time. The probability distribution for DVD rentals per customer at Video To Go is given below. There is 5 video limit per customer at this store, so nobody ever rents more than 5 DVDs.
| x | 0 | 1 | 2 | 3 | 4 | 5 |
| P(X=x) | 0.03 | 0.50 | 0.24 | ? | 0.07 | 0.04 |
Another shop, Entertainment Headquarters, rents DVDs and videogames. The probability distribution for DVD rentals per customer at this shop is given below. They also have a 5 DVD limit per customer.
| x | 0 | 1 | 2 | 3 | 4 | 5 |
| P(X=x) | 0.35 | 0.25 | 0.20 | 0.10 | 0.05 | 0.05 |
Partial Answer:
A: X = the number of DVDs a Video to Go customer rents
B: 0.12
C: 0.11
D: 0.77
A game involves selecting a card from a deck of cards and tossing a coin. The deck has 52 cards and 12 cards are "face cards" (Jack, Queen, or King)The coin is a fair coin and is equally likely to land on Heads or Tails
The variable of interest is X = net gain or loss, in dollars
The face cards J, Q, K (Jack, Queen, King). There are(3)(4) = 12 face cards and 52 – 12 = 40 cards that are not face cards.
We first need to construct the probability distribution for X. We use the card and coin events to determine the probability for each outcome, but we use the monetary value of X to determine the expected value.
| Card Event | $X net gain or loss | P(X) |
| Face Card and Heads | 6 | (12/52)(1/2) = 6/52 |
| Face Card and Tails | 2 | (12/52)(1/2) = 6/52 |
| (Not Face Card) and (H or T) | –2 | (40/52)(1) = 40/52 |
You buy a lottery ticket to a lottery that costs $10 per ticket. There are only 100 tickets available be sold in this lottery. In this lottery there is one $500 prize, 2 $100 prizes and 4 $25 prizes. Find your expected gain or loss.
Start by writing the probability distribution. X is net gain or loss = prize (if any) less $10 cost of ticket
| X = $ net gain or loss | P(X) |
| $500–$10=$490 | 1/100 |
| $100–$10=$90 | 2/100 |
| $25–$10=$15 | 4/100 |
| $0–$10=$–10 | 93/100) |
Expected Value = (490)(1/100) + (90)(2/100) + (15)(4/100) + (–10) (93/100) = –$2. There is an expected loss of $2 per ticket, on average.
A student takes a 10 question true-false quiz, but did not study and randomly guesses each answer. Find the probability that the student passes the quiz with a grade of at least 70% of the questions correct.
A student takes a 32 question multiple choice exam, but did not study and randomly guesses each answer. Each question has 3 possible choices for the answer. Find the probability that the student guesses more than 75% of the questions correctly.
Suppose that you are perfoming the probability experiment of rolling one fair six-sided die. Let F be the event of rolling a "4" or a "5". You are interested in how many times you need to roll the die in order to obtain the first “4 or 5” as the outcome.
A: X can take on the values 1, 2, 3, .... p = 2/6, q = 4/6
B: 0.2222
C: 3
**Exercises 38 - 43 contributed by Roberta Bloom
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